Writing a polynomial function in sigma notation

Question

I've been working on a problem and I finally found the polynomial (seen below) that describes the function $ln(1-2x^2)$. Now I have to write:

in sigma notation but I really can't seem to get it.

Answer 1

This is simply $\ln(1-y)$, where $y=2x^2$. $$\ln(1-2x^2)=-\sum_{i=1}^\infty \frac{(2x^2)^n}n=-\sum_{i=1}^\infty \frac{2^nx^{2n}}n$$