## anonymous one year ago Confirm the integration formula by integrating the appropriate Maclaurin series term by term. \int e^xdx=e^x +C

$e^x=\sum_{n=0}^\infty \frac{x^n}{n!}~~\implies~~\int e^x\,dx=\sum_{n=0}^\infty \frac{x^{n+1}}{(n+1)n!}+C=\sum_{n=0}^\infty \frac{x^{n+1}}{(n+1)!}+C$ This almost matches the sum on the left except for $$n+1$$ in place of $$n$$. How can you adjust this?