Question

Find the sum of the series

Answer 1

\[\sum_{n=1}^{\infty} \frac{ 3^nx ^{2n} }{ 4^{n+1} }\]

Answer 2

@Loser66

Answer 3

Um, you're given a power series... are you supposed to find the "summing" function? Or are you looking for the radius of convergence?

Answer 4

I found the radius of convergence to be 2/sqrt(3). Need to find sum S of the series.

Answer 5

@Hero

Answer 6

you need to find a way to sum up a power series...I am sure your book has some suggestions yes?

Answer 7

Okay, well try comparing it to the following,
\[\frac{1}{1-x}=\sum_{n=0}^\infty x^n\]
\[\begin{align*}\sum_{n=1}^\infty \frac{3^nx^{2n}}{4^{n+1}}&=\frac{1}{4}\sum_{n=1}^\infty \left(\frac{3}{4}x^2\right)^n
\end{align*}\]
How would you write this like the first known series?