Find the power series representation centered at x=0x=0x=0 for f(x)=ln(1+x2)f(x) = \ln(1+x^2)f(x)=ln(1+x2).
∑n=1∞(−1)n−1x2nn\sum_{n=1}^{\infty} (-1)^{n-1} \frac{x^{2n}}{n}∑n=1∞(−1)n−1nx2n
∑n=0∞(−1)nx2n+2n+1\sum_{n=0}^{\infty} (-1)^{n} \frac{x^{2n+2}}{n+1}∑n=0∞(−1)nn+1x2n+2
∑n=1∞x2nn\sum_{n=1}^{\infty} \frac{x^{2n}}{n}∑n=1∞nx2n
∑n=0∞(−1)nxnn+1\sum_{n=0}^{\infty} (-1)^{n} \frac{x^{n}}{n+1}∑n=0∞(−1)nn+1xn