1. ## [SOLVED] Geometric Series

K=0 to Infinity Where (-1)^K( X^2K+1). I cant figure out how to the get exponent on X to only be K

Thanks 4 any help!

2. Hello, nikie1o2!

$\sum^{\infty}_{k=0} (-1)^k x^{2k+1}$

I cant figure out how to the get exponent on $x$ to only be $k.$
. .
I don't know what this means . . .
In fact, you haven't told us what we're supposed to do . . .

Write out the series: . $S \;=\;x - x^3 + x^5 - x^7 + x^9 - \hdots$

We have a geometric series with first term $a = x$ and common ratio $r = -x^2$

If $|r| < 1$, the series will converge.

And its sum will be: . $S \;=\;\frac{x}{1+x^2}$

Is that any help?

3. Originally Posted by Soroban
Hello, nikie1o2!

In fact, you haven't told us what we're supposed to do . . .

Write out the series: . $S \;=\;x - x^3 + x^5 - x^7 + x^9 - \hdots$

We have a geometric series with first term $a = x$ and common ratio $r = -x^2$

If $|r| < 1$, the series will converge.

And its sum will be: . $S \;=\;\frac{x}{1+x^2}$

Is that any help?
Thats the correct answer in my textbook. thank you! I was thrown off because my professor said that "a" couldnt be a variable? I guess she was wrong