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So would I write the sum as \[\sum_{n=1}^{\infty} (-1)^{n} (x)^{2n+1}\]

you need a 2 inside the parentheses

I thought power series was just sum x^n

well the representation

converges if \(|2x|<1\) i.e if \(|x|<\frac{1}{2}\)

Ah So i just take it right away. Makes sense. Thanks a lot^^

also you should start your summation at \(n=0\) i think

to be more precise i guess if converges if \(|2x^2|<1\) but same answer