Power Series - Made Easy! | Power Series Representation of a Function | Math with Professor V

How to find the power series representation of various functions MADE EASY! I break down the process into 3 main cases, and work through lots of examples so that you can become a professional at mastering this concept as well.
Need more help with sequences and series? Check out my other video lectures already on my KZbin Channel:
Power Series: • Calculus 2: Power Seri...
Representation of Functions as Power Series:
• Calculus 2: Representa...
• Calculus 2: Differenti...
Finding Taylor and Maclaurin Series for Functions: • Finding Taylor and Mac...
Calculus 2 Video Lectures: • Calculus 2 Video Lectures
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Professor V
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Calculus 2 Lecture Videos on Integration:
Integration by parts: • Calculus 2: Integratio...
Tabular Integration: • Integration by Parts -...
Trigonometric integrals: • Calculus 2: Trigonomet...
Trigonometric Substitution: • Calculus 2: Trigonomet...
Partial Fraction Decomposition: • Calculus 2: Integratio...
Strategy for Integration: • Calculus 2: Strategy f...
Improper Integrals: • Calculus 2: Improper I...
Trig Review:
Unit Circle: • Trigonometry: Circular...
Trig Identities: • Precalculus: Trigonome...
Sum and Difference Formulas: • Precalculus: Sum and D...
Double Angle & Half-Angle Formulas: • Precalculus: The Doubl...
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[@fannie_zhao4075]

At 12:37 isn't it 2^(4n +4) instead of +2?

[@mathwithprofessorv]

Yes! Thanks for catching that! Whoops 😬

[@ashleycook1174]

I have not been able to find a video on this concept that was so well-explained, thorough, and REASSURING. It's one thing to understand the material and make a video about it, but it's another thing to be able to teach it as thoughtfully as you did. Thank you SO much.

[@mathwithprofessorv]

You are so very welcome! Thank you for your comment-I truly appreciate it! ☺️❤️❤️❤️ I put my heart into teaching math and it brings me such joy and fulfillment when I hear feedback like yours. Wishing you lots of success!!!

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[@mathwithprofessorv]

Thank you so much for your incredibly kind words-it means a lot to me since I’m passionate about what I do and want to make learning calculus as easy and accessible as possible for my students and students around the world. ☺️

[@mistermeatballs7800]

I haven't found a more concise explanation for power series representation online than this - this is really well done, liked and subscribed

[@mathwithprofessorv]

Thank you so much for your support and kind words!!!! 🙏🏻☺️

[@koala1578]

You're so right mistermeatballs7800

[@minhluanne7462]

agree with u

[@santaclaus2480]

Isn’t there an error in q3 distributing ( 2^4)^(n+1)? Should it not be (2)^(4n+4)?

[@davytong3157]

I was having an anxiety attack because I couldnt figure out how to do this, not only did you explain everything perfectly and answered all my questions, you assured me and made me feel okay, thank you

[@mathwithprofessorv]

Of course-it is an honor! Comments like yours make me know this is all worth it and I’m doing what I’m supposed to do. You are more than capable of mastering this topic, and a professor who understands it thoroughly can explain it in an understandable way that isn’t intimidating. Wishing you lots of success!!! ☺️☺️☺️🫶🏻🫶🏻🎉

[@arosdeluna]

this is the best video of Power Series Representation of function in youtube, thank u so much, this was very helpful for studying

[@mathwithprofessorv]

You’re so welcome!!!! Thank you for your kind words 🙏🏻🙏🏻🙏🏻💕

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I was literally scribbling all over my homework panicking again, because I did not understand this at all from the class I had. After watching this video omg I feel so much better! It's because of people like you offering this help on youtube for free that one day I'll be able to get my engineering diploma. Thank you so much!

[@mathwithprofessorv]

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Genuinely an amazing way to get this topic down. Just straight to the point

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Well done. The lecture is very clear. No confusion.

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I was stressing so bad about this because I didn't understand it at all and I have a test on it tomorrow. Thank you so much this genuinely got me from not understanding it at all to fully understanding it. THANK YOU

[@mathwithprofessorv]

Glad it helped! You are most welcome. 🤗

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Awesome technique! Thanks for sharing

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[@mathwithprofessorv]

Thank you 🙏🏻 I so appreciate your comment and support!!! Feel free to share and subscribe ❤️

[@randomcalculusstudent]

I found this section to be so confusing, but your examples helped so much!! The way you showed how the differentiation and integration was so clear and helpful. You saved my Calc 2 grade thank youuu. Liked and subscribed!!

[@mathwithprofessorv]

I'm so glad! 😀

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you make learning this actually fun with your personality, thank you.

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made it to the end, super helpful, thank you so much

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[@mathwithprofessorv]

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[@mathwithprofessorv]

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best video on power series representation!!!

[@mathwithprofessorv]

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[@mathwithprofessorv]

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this is the best tutorial for power series representation!!! Thank you so much, I was so confused before watching this video ❤

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this is exactly what i needed, thank you

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I'm so glad! 😃

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I was so lost and confused with power series. This really helped me, thank you!

[@mathwithprofessorv]

You’re welcome!!! Happy to help!

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[@mathwithprofessorv]

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you explain so cool! the way you made it into 3 groups was great so now ik what to do while going through problems

[@mathwithprofessorv]

Oh I’m so so glad!!!! It makes the topic so much more manageable, right? ☺️

[@melikare1530]

absolutely! i have a question. what should we do when they want us to do this in reverse? like when we are given what we got as an answer here and wanting to turn it back to the function? (sigma to function as in finding the sum instead of going through function to sigma)@@mathwithprofessorv

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[@azrayns]

Hello. Can a sum series in the form an.x^n have a convergence interval (-3/2,+3/2]? There was such a question in our exam, do you have any idea how to solve such questions?

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[@mathwithprofessorv]

Thank you so much 😀 You’re very welcome!

[@nickchandra4890]

Thank you. I am struggling to apply this to e^x/(1+3x)^2

[@user-jx5bg1cl6q]

Thanks alot ❤

[@mathwithprofessorv]

You’re so welcome!

[@pobo-]

thanks for teaching me 🌷

[@pobo-]

it's actually 2^(4n+4) around 13:15 but it's a small calculating mistake

[@mathwithprofessorv]

My pleasure 😊

[@ishaanbaruah8968]

At 25:22 is it (-1)^(n+2)? since we subtract one from the index and add 1 to all the n terms in the series?

[@davidlightfoot3217]

Genuinely think this video saved my test grade. Thank you. This was so much clearer than anything I've seen thus far. Breaking down how you got to every step and thoroughly explaining everything is extremely helpful. Every other video I've seen and even my professor just fly through everything. So once again, thank you!

[@mathwithprofessorv]

You are most welcome! Happy to help. Please share and subscribe, it would mean so much to me. ☺️🙏🏻

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I did make it to the end, and I WILL be explaining the power series to my barista, in your honour.

[@mathwithprofessorv]

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[@vidyadharkottisa8367]

Great

[@wz6952]

This is very helpful. The rest of power Series videos on youtube are terrible for some reason.

[@mathwithprofessorv]

Because they’re not by Professor V! 😎

[@valrrrie]

perfection

[@mathwithprofessorv]

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[@mathwithprofessorv]

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Ghaint beautiful explanation from india (Punjab)

[@mathwithprofessorv]

Thank you so much! ☺️

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God bless you!

[@mathwithprofessorv]

Thank you so much! ☺️🫶🏻

[@DraftingCADemy2023]

what would be its interval @20:49

[@Yuna-wt4ny]

❤❤❤

[@satellite1975128]

At 30:16, the denominator inside the sum should be 5^n, not 5^n+1. I used this to help with some homework and it didnt work with 5^n+1, but did work with 5^n even with n=0...

[@mathwithprofessorv]

No, you’re incorrect. I brought the 5 outside of the sum inside with 5^n, making it 5^(n+1).

[@Sanda.iTUBEvideos]

❤

[@morenoclr]

10:14

[@santaclaus2480]

Isn’t there an error in q 3? Shouldn’t the distribution of( 2^4)^(n+1) be 2^(4n+4) not 2^(4n+2)?

[@mathwithprofessorv]

Yes, I addressed it in a comment a while back but now I pinned it so everyone can see. Good catch!

[@luvochiya4134]

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[@mathwithprofessorv]

🤣🤣🤣🤣🤣 You’re very welcome!

[@msawawa_sa9794]

I'm a trooper i made it to the end..

[@mathwithprofessorv]

Yay!!!! Thanks for your support! Hope you are a boss at power series now 👍🏻☺️

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Im a trooper thanks boss maam

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I am a trooper and I made ut to the end🎉

[@mathwithprofessorv]

Yay congratulations!!!! Thanks for letting me know! ☺️🙌🏻🙌🏻🙌🏻

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