Shoutout to the classroom for also being confused when I'm confused.

If you're like me and reviewing for an exam, here are some time stamps! Steps for solving Infinite Series: 19:20 Geometric Series: 51:20 Harmonic Series: 1:28:03 Divergence Test: 1:51:08

Between his clever humor, delivery/ enunciation, and clear concise breaking down of steps. This man deserves an award. At least from youtube or something. My calculus 2 teacher is the COMPLETE OPPOSITE of Prof. Leonard. Gets mad when you ask questions and doesn't explain things clearly and doesn't seem to care about the well-being of us students. As an aspiring math teacher to be, you are a great role-model and I hope I can be half the teacher you are.

Introduction to Series 0:00 Telescoping Series 27:20 Geometric Series 51:20 Harmonic Series 1:28:05 Divergence Test 1:40:00 Properties of Convergent Series 1:42:11 The rest is just more examples

Not only are Leonard's videos a godsend but so is the replay button.

My college professor is a very nice person but presents material in a very disorganized manner. I've been struggling through Calc 2 by watching youtube videos, reading the book, and visiting Khan Academy and your lectures have been such a huge help. I just wanted to say thank you. Thank you!

Please live forever. You helped me so much and I can only imagine the good you would do with an extra hundred years or so.

There is nothing so valuable to math understanding like a Socratic, conversational style of teaching. Personally, I don't think I would have ever understood series if it wasn't taught the way it was on this video. The first 17 minutes of this video were eye-opening to me and once I saw WHY the existing (converging) limit of a partial sum HAS to be the actual sum of an infinite series I stood in awe of the paradoxical simplicity and depth of this topic. This is the beauty of numbers at work. Professor Leonard, you just added to my love of mathematics today. Thank you.

got a 100% on my first calc II exam,, first time taking a math course in nearly 10 years,, thanks professor leonard! owe it to you

He's literally so nice. His lectures are like ASMR, as in his delivery, his humor, his niceness - genuine concern whether his students understand, his super detailed explanations. I laugh when he makes a joke and instinctively raise my hand whenever I get a problem. I love how he goes over basic algebra becaue I'm not too fast, like I can't see the steps in my head.

I actually raise my hand every time you say so..

He is probably the best teacher at math I have ever seen. 100X better than my calc 2 professor now. This is definitely my 'go to' for calc 2. Maybe I will get higher than a 40% for my next exam learning from him instead of my professor now...

I hope to become a math lecturer one day. Professor Leonard is such an inspiration.. He explains very well and seems to have a real passion for teaching in general. What a legend!

I honestly don't get how you make this so easy to understand.

I don't go to lectures, I only watch Professor Leonard

Professor Leonard you are fantastic. I'm seriously starting to doubt the quality of education I'm currently paying for at Iowa State University after seeing what a great professor is like and what I have been missing.

PROFESSOR LEONARD IS THE BEST, HOPE ALL THE LECTURES WOULD JUST LEARN FROM HIM.

Series and sequences have been the first time studying math where I have broke down from pure frustration. Thank you for taking the time to teach us this the way it should be taught!

Professor Leonard is an awesome supplement to my class. My teacher is pretty good, but I often need to listen to it a second time, so i just put it on 2 times the speed and I understand that material fairly well.

My professor goes extremely fast, you explain these concepts so well and very slowly to ensure understanding. Thank you for uploading these videos!!! I was beyond lost, 1 hour and 30 minutes into this lecture and everything is so clear to me. Thank you Professor Leonard!!

Awesome work on this video! I wish I had more professors like you. You make calculus fun and engaging, which is... difficult, to say the least. The Calc II professor in my 3 1/2 hour night class is a complete snore, and I don't learn half of what I learn from you. Honestly, I don't understand why your students don't laugh at half of your jokes. I thought they were hilarious! Whether they react or not though, you should know that you infuse a fairly dry course with just the right amount of juiciness. Don't change a thing about your style.

mate you scared the shit outta us with that smile after "I'M NOT GONNA LIVE FOREVER, OR AM I?"

Difference between you and my current professors: They only teach me how to do something, you help me understand WHY I'm doing something and THEN show me how to do something properly. Your lessons always stick with me, Professor Leonard, other professors' lessons never do! They always go right over my head. Thank you for what you do!

Thank God you exist. Thank you so much for the knowledge, Professor.

YOU ARE THE KING OF CALCULUS.. THANK YOU SO MUCH FOR THIS EXPLANATION PROFESSOR LEONARD!!!!!!!!

You are really gifted in the field of lecturing PROFESSOR LEONARD. I rank you above all the mathematics teachers I've seen so far. I feel extremely happy anytime I learn from your lessons. Only God can reward you for your contributions. I wish you the best in the world and best of guidance for the success of the hereafter. wish you all the best and I can't stop thanking you so much. welldone SİR.

Professor Leonard, thank you for an amazing video/lecture on the Introduction to Series, Geometric, Harmonic Series and the Divergence Test in Calculus Two. Pattern recognition is important when analyzing series in Mathematics. I also encountered series in Digitel Signal Processing and Signal and Systems Theory.

You are saving my university grades. THANK YOU!!!

I wish I would have found your channel sooner! you make everything soooooo clear!!!! THANK YOU!!!!

"You're never free. You only think you're out of the matrix." As soon as he said that, I thought of Linear Algebra.

For those that don't get it the 1st time, you may wanna watch it again. Definitely made more sense the 2nd time for me. Good luck to all and THANK YOU PROFESSOR LEONARD!

If I want step-by-step, thorough explanations, this is the channel I go to! Thanks!

I have learned so much from Professor Leonard. I believe he is the best teacher in the world. My college teacher was so worst and I could not pass the exam, so I could not sleep and was going to die.In the hospital, I got Leonard's lecture.His lecture saved my lecture. He is not only my good teacher but also my life.Now I am having a happy life and math is so easy for me.Anyway my major is math.

Your videos have allowed me to learn a lot of calculus 2 material before I've even started the class. Just wanted to say thank you! You're a great teacher.

While I never had him as a professor in real life, still one of the best profs I've experienced thus far

Your videos are a blessing. I don't care for my calc teacher too much, but I really enjoy your videos. You're engaging and you explain the why and how much better. I really appreciate it.

I'm doing an independent study of Calc II and these videos are immensely helpful!

You're truly a blessing. I hope your videos never get taken down

Awesome, He is a Rock Star in teaching Mathematics.!! I become a fan for him now.. he just teaches complex stuff and makes us understand on the first go.., unbelievable Man. Lots of respect , because u just teaches the subject in the most beautiful way and NOT show off the knowledge gained ( most average professors do this mistake.)

professor...please..please...teach calc 3. and discrete. and linear algebra.

I am a senior in high school preparing for the AP Calculus BC exam, which is the equivalent of Calculus II by myself and I couldn't get any better help than your videos, thank you so much!!

You are a gentleman and a scholar.

Thank you so much for these videos! I love mathematics and I've always loved them since little but since the introduction of limits, maths started taking a downturn for me due to the surge of mental issues and my current teacher, who acts entitled in every way shape and form, doesn't help the fact I'm struggling. Still, I find your videos to be a salvation, really! You present this in such a friendly and caring manner, interacting with the classroom and so on, it feels like I'm back in my first 'highschool', which is called Secondary School in my country, year once again and I just love listening to these in the background as I do exercises or take a break from solving them to clear my thoughts and review the topics I just practised. Thank you so much for these! They are helping me through really hard times!

You are a fantastic professor. Thank you so much for posting these, they are extremely helpful. I wish more professors had your passion and skill for teaching.

Thank you SO much for sharing this video with the world's Calculus students. It really helps to have someone clearly explaining these concepts at a reasonable pace.

Professor Leonard, you are a college student life saver lol. I mean your lectures are sooooooo clear. Thank you for taking your time to post these videos.

Missed a lesson in Calc 2 the other day on Series, and I'm so glad I remembered this videos! I'm already s refreshed, and learning much more than I do in class! Thanks a bunch!

شكرا مستر ليونرد thanks Professor Leonard .

I love that the partial fraction decomposition turns perfectly into a telescoping series. Brilliant!

I have a Calc 2 exam on Monday and have really fallen behind, thanks so much for these videos they really explain the topics so much better!

Thank you for making these videos. You've made series make sense for me and helped me pass my Calc 20B class. I can't express my thanks enough for you putting these videos up for others to see.

You're the man Professor Leonard! Your classes are so much clearer than mine at my University. Thanks for sharing!

Went from understanding nothing to feeling like I mastered this topic thanks so much

You are an amazing teacher. I have college professors who do not explain these math concepts as well as you do. Thank you for posting your lectures.

I'm retaking calc 3 on this upcoming spring and all these god blessing videos are really helping me out to prepare for passing course this time. As always, thank you for filming and posting such a wonderful lectures. Seriously god bless you

Thank you Professor Leonard. I do not know how I will do on my test, but I feel really good about Calculus 2 because of you. Thank you so much.

i do not know if you will ever see this but whatever, you are amazing... god bless you.

THANK YOU SO MUCH FOR ALL THE VIDEOS IN THE COURSE! They have been so helpful for me to understand all the material of Calculus 2! You are really good at explaining and it is easy to see how dedicated you are to your job and your students!!

I can't thank you enough professor Leonard for making me love calc 2. i love the full detailed steps. thank you again.

Just stumbled on this playlist half way through a self directed online course through Matlab. Wish I knew about it sooner. Great teacher. Already looking forward to watching these lectures for calc 3 and diff eq. Props

This is a really high quality presentation of series. Thanks a lot -- and I'm using this video for a real analysis class, which is saying something about the quality of your treatment of this topic.

Thank you professor Leonard, I've been watching your videos all through calc 1 and now 2.

You really put your heart into these lectures.

Professor Leonard, you're an excellent professor and I'm so thankful for your videos! It's sad that I learn more from you than from the university I pay thousands to attend....

Thank you very much , i always feel good after watching your videos and it seems tht i will get A+ on Calculus , i wish i have such a professor at my university))

Thank you for the thoughtful and articulate instructions. I feel like I will be able to pass Calculus 2 with the help of your videos!

My lectures are cancelled due to coronavirus, so this is SUPER needed thank you Professor Leonard

My caluculus proffessor is teaching this stuff so fast that i can't understand anything. Thanks to you Prof. Leonard, i understand what calculus is about. Please do more videos.

Have an exam in about 4 hours. I think you just saved my grade! Thank you!

You are the best teacher I have ever seen...thanks for your free service... please keep teaching like this for years and years...thanks

I cannot express enough the magnitude of my gratitude to you. Thanks. The only thing I hate are the jelly-bellies answering the simplest of your questions AFTER you had given the correct answer and had repeated it twice.

People like yourself should be offered a doctorate in teaching or something similar. You offer way much more than most that have a PhD. I understand that a PhD has a lot to do with research, but you have clearly researched and put a very popular and successful teaching method into practice.

Thank you for these amazing videos. I wish more professors taught like you.

Love these lectures; they give you a good intuitive grasp of mathematics! Just what you need when you are a physics student!

Thank you so much, you are amazing. My teacher had notes saying that a series is a bunch of partial sums but we didn't go into why. I come to your videos and you have all the answers. You are amazing

Professor Leonard is really really really the best teacher in the world. And he has saved my life and dream

Thank you.. I've spent countless hours reading the calc textbook and learned nothing. And when I watched your video, I understand it right a way! Thank u! :) Your awesome! I wish your our teacher!

your WAY BETTER than my cal 2 teacher, I go to his lectures to sign roll and watch your lecture on my phone

Just finished my calculus 2 exam , it was easy like a piece of cake thank you professor really . Best wishes from Palestine

4:45 is the reason I've watched all your videos, you SUM up (pun intended) information and recap to make sure we follow! thanks so much! cheers from Montreal, Canada

thanks for this special lecture. It helps me to pass my Midterm exam. You're so great

Awesome, you are a great Teacher, I am doing online school through ASU, and your lectures are awesome for when I need an in depth description of a subject.

I do not know how to say that but I wanna thank you I just saw my calc 2 grade and I passed the class.You are on of the reason that made me pass the class. thak you very very much professor you are the best!!!

thank you thank you thank you , you saved my LIFE it's a very hard section in calc2 but your lectures clarified Everything , it is time consuming but at the end it all makes sense , thank you !!

Thanks a lot Leonard, you explain everything in a very understandable way.

Prof. Leonard Everything make sense to us, thank you very much

My Calc two teacher is very theoretical, he's great don't get me wrong, but I have to first watch Professor Leonard's videos to understand my current teacher's videos. I've been watching Professor Leonard's videos since before calculus. Excellent teacher.

I wish my teachers could explain like you. That was really amazing..💖

Great teaching! Your videos are long, but well worth the time. Thank you.

Thank you so much for posting videos !!!!! You are a great professor :) Now everything makes sense ....

Watching these again to review before my final, thanks for all your help this semester

I love the way you teach and I thank you so much for uploading your lectures.

phenomenal. Thank you Professor Leonard for "dumbing it down" far enough for even a d.a. like myself to understand! Makes it look easy!

Thank you so much. I'm currently in Calc 2, which we use Learning Modules (flipped class), and I'm dying. This makes so much more sense. Thank you!

I had so much trouble with telescoping series until watching this video. Thanks for explaining everything so clearly!

I wished my Professor could explain calculus like you, thank you very much!

professor you are an amazing person and I appreciate all of your hard work

Love your classes! You're an awesome teacher!

Thank you sooooo much!!!!! I used to get frustrated reading my book and trying to get this, but now it seems so simple! :D

I'd consider myself to be someone with a slight attention span problem, but I was able to watch this is a solid 2 sittings & I understand so much now!!