Determine the Taylor series for f(x)=∫0xe−t2dtf(x) = \int_0^x e^{-t^2} dtf(x)=∫0xe−t2dt centered at 000.
∑n=0∞(−1)nx2n+1n!(2n+1)\sum_{n=0}^{\infty} \frac{(-1)^n x^{2n+1}}{n!(2n+1)}∑n=0∞n!(2n+1)(−1)nx2n+1
∑n=0∞(−1)nxnn!\sum_{n=0}^{\infty} \frac{(-1)^n x^{n}}{n!}∑n=0∞n!(−1)nxn
∑n=0∞(−1)nx2nn!\sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{n!}∑n=0∞n!(−1)nx2n
∑n=0∞x2n+1n!(2n+1)\sum_{n=0}^{\infty} \frac{x^{2n+1}}{n!(2n+1)}∑n=0∞n!(2n+1)x2n+1