General question about Taylor Series

[Blitze105]

Hello,
I have a test tomorrow in calculus 2, and atm we are studying Taylor series. This isn't too complicated for my understanding; however, there is a little tip on the bottom of my outline for the test that says:

Extra Credit: Summing of a series, using its connection to a Taylor Series

Anyhow know what i could look up to find an example of this? I can't seem to find anything on Google...
I'm guessing i'll have a series... and convert it to a Taylor series, and then find the sum depending on whether it is finite or infinite...
If any one could shed some light on this i would appreciate it...
~Blitze

 

[galactus]

If I understand correctly, you could find the sum of, say, \(\displaystyle \sum_{k=1}^{\infty}\frac{k^{2}}{4^{k}}\)

Differentiate the MacLaurin series for \(\displaystyle \frac{1}{1-x}\), multiply by x, differentiate, multiply by x again.

 

[greekcalcbeast]

With professor Benofy...yea, i have some friends in that class and they are currently asking me for help. they asked me to google that question