How To Find A Power Series By Differentiating

How To Find A Power Series By Differentiating
We find the power series of f(x) = 5/(1 + x)^3 centered at c = 0 via differentiation of an infinite geometric series.
Please Subscribe here, thank you!!! goo.gl/JQ8Nys

[@marc1476]

Ahhh this is perfect! I've been on youtube for more than an hour trying to find a video that could explain this to me but all of them were too complicated and long. Thank you for this!

[@TheMathSorcerer]

np!!

[@dantheman826]

out of all the videos... you were the best at explaining each step

[@TheMathSorcerer]

thanks man:)

[@Patrick-S3]

I spent FOREVER looking for a video that explained these problems well enough for me to understand. This was perfect.

[@TheMathSorcerer]

Yeah this is a tough one to explain! I am glad it helped someone!

[@arnavverma2135]

Nice! 7 years later, this is still helpfull.

[@skillzpunk]

Helped a lot couldnt find an example using differentiating, then found your video. Thank you

[@TheMathSorcerer]

Jack Goldman Np, very glad it was helpful!

[@robbieschmidt4868]

Top tier, wish u were my calc teacher

[@Trump_Gaming]

Don't you have to integrate the power series twice at the end since you took two derivatives of f(x)? Or do you just leave it like that?

[@lesegomokgabudi5798]

God bless you..... thanks a lot

[@SlowKlone]

what if its 5+x instead of 1+x, i can't find a single video showing that version

[@cosmickitty9533]

Thank you so much!!!!

[@TheMathSorcerer]

np:)

[@lesegomokgabudi5798]

THANKS BRO

[@lucabortolotti9587]

I'm way too late, but if someone is nice enough in the comments? My question is: how do you find the series of a function, but not centered in 0 (for instance centered in i or -2 or whatever)?

[@TheMathSorcerer]

it depends on the function, you can find the taylor series of a function centered at x = c using the formula, a_n = f^(n)(c)/n!, the series is then f(x) = sum( a_n (x - c)^n, n = 0, 1, ...). That's one way, it's long and tedious usually. Sometimes you can use 1/(1 - x) = sum(x^n, n = 0, 1, ...) also. I just realized I did that in this video except it was c = 0. Here is an example with c = 3 kzbin.info/www/bejne/n5O3eYxsrtdoacU&list=PLO1y6V1SXjjMkSvC2kY351GGK8R5JN3KQ Here is a taylor series example(I don't think that's what you want though, but here it is anyways in case) kzbin.info/www/bejne/iZTQgJuhaJaen9U&list=PLO1y6V1SXjjMkSvC2kY351GGK8R5JN3KQ

[@lucabortolotti9587]

@@TheMathSorcerer I wasn't expecting such a quick answer, ty very much for your help!

[@TheMathSorcerer]

:)

[@zhengyangsong]

Really useful! Thanks a lot!!!!!!!!!!

[@byJayzik]

Thanks! Just wish you told us how to check the radius of convergence

[@Danazstr]

b-a/2

[@cynthiamih632]

This is a good one ! Many others you have no idea what they are doing !

[@TheMathSorcerer]

thx!!!

[@RamonaPyke-n4h]

THANK YOU!! this is incredibly helpful I am studying for my Calc2 final and I had yet to find a video that explained clealry and easily how to do this. Thank you so much

[@timavilov8712]

THANK YOU!! this is incredibly helpful. This is not explained at all in my class

[@kendalwilliams5128]

Thank you! this helps a ton

[@kevinortiz809]

God bless you, idky no one else has this example

[@TheMathSorcerer]

[@zanon9148]

Thank you very very mutch, helped a lot!

[@inj1979]

Thanks

[@sudden4110]

You have no idea how much this video helped, thank you very much!

[@TheMathSorcerer]

yay glad it helped!!