exo7 4581

$\sum_{n=0}^\infty \frac{x^n}{2n-1}$.

$\sum_{n=0}^\infty n^2x^n$.

$\sum_{n=0}^\infty n^3x^n$.

$\sum_{n=0}^\infty \frac{x^n}{(n+1)(n+3)}$.

$\sum_{n=0}^\infty \frac{(-1)^nx^{2n+1}}{4n^2-1}$.

$\sum_{n=0}^\infty \frac{x^n}{4n-1}$, $x\ge0$.

$\sum_{n=0}^\infty \frac{n+3}{2n+1}x^n$.

$\sum_{n=1}^\infty \frac{x^n}n\ch(na)$.

$\sum_{n=0}^\infty \frac{n\sin^2(n\theta)}{2^n}$.

$\sum_{n=0}^\infty \frac{n^2+1}{n+1}x^n$.

$\sum_{n=0}^\infty \frac{x^n}{(2n)!}$.

$\sum_{n=0}^\infty \frac{\sin^2(n\theta)}{n!}x^{2n}$.

$\sum_{n=0}^\infty \frac{n^5x^n}{n!}$.

$\sum_{n=0}^\infty \frac{x^{3n}}{(3n)!}$.

$\sum_{n=1}^\infty C_{2n}^{n+1} x^n$.

$\sum_{n=0}^\infty \frac1{n!} \int_{t=1}^x\ln^nt\,d t$.

$\sum_{n=1}^\infty \left(1+\frac12+\dots+\frac1n\right)x^n$.