Alternating Infinite Series Calculator

This application find the summation of alternating infinite series \[\sum_{n=n_0}^\infty (-1)^n a_n\] where $n_0\geqslant 0$ is the starting index and $(-1)^n a_n$ 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 $\sinh$, $\cosh$, $\tanh$, $\sin$, $\cos$, $\tan$, $\exp$, $\mathrm{pow}$, $\mathrm{abs}$, $\mathrm{sqrt}$, $\log$.

As an example, let us find the summation of $\displaystyle\sum_{n=1}^\infty \frac{(-1)^{n-1}}{n}$. We have as the input to the calculator $n_0=1$ and $\displaystyle a_n=\frac{1}{n}$, noticing that $(-1)^n$ is not included in the input data. Then we get 0.693147180559946 as the result.

Alternating Infinite Series Calculator