Infinite Series Calculator

This application find the summation of convergent infinite series \[\sum_{n=n_0}^\infty a_n\] where $n_0\geqslant 0$ is the starting index and $a_n$ is the $n^\text{th}$ term of the series. Here are some examples of $a_n$: $\displaystyle\frac{\cos(n\pi)}{n^4}$, $\displaystyle\frac{1}{2^n n}$, $\displaystyle\frac{3+2n}{2^n}$, etc. A math expression of $a_n$ can contain the following 11 functions $\sinh$, $\cosh$, $\tanh$, $\sin$, $\cos$, $\tan$, $\exp$, $\mathrm{pow}$, $\mathrm{abs}$, $\mathrm{sqrt}$, $\log$.

Note that this calculator failed to find the summation of some convergent infinite series or the result does not reach the accuracy criteria. The examples of these series are $\displaystyle\sum_{n=1}^\infty\frac{1}{n^2}$ and $\displaystyle\sum_{n=1}^\infty\frac{(-1)^{n-1}}{n}$. However, other calculators can be used for these series evaluations, Riemann Zeta Function for the first and Infinite Alternating Series Calculator for the latter.

Infinite Series Calculator