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!
Hello, nikie1o2!
In fact, you haven't told us what we're supposed to do . . .$\displaystyle \sum^{\infty}_{k=0} (-1)^k x^{2k+1}$
I cant figure out how to the get exponent on $\displaystyle x$ to only be $\displaystyle k.$
. . I don't know what this means . . .
Write out the series: .$\displaystyle S \;=\;x - x^3 + x^5 - x^7 + x^9 - \hdots$
We have a geometric series with first term $\displaystyle a = x$ and common ratio $\displaystyle r = -x^2$
If $\displaystyle |r| < 1$, the series will converge.
And its sum will be: .$\displaystyle S \;=\;\frac{x}{1+x^2}$
Is that any help?