# Series and Sum Calculator with Steps

This calculator will try to find the infinite sum of arithmetic, geometric, power, and binomial series, as well as the partial sum, with steps shown (if possible). It will also check whether the series converges.

## Answer

**Your input: calculate $$$\sum_{n=1}^{\infty} 3^{- n}$$$**

$$$\sum_{n=1}^{\infty} 3^{- n}$$$ is an infinite geometric series with the first term $$$b=\frac{1}{3}$$$ and the common ratio $$$q=\frac{1}{3}$$$.

By the ratio test, it is convergent.

Its sum is $$$S=\frac{b}{1-q}=\frac{1}{2}$$$.

Therefore,

$$\color{red}{\left(\sum_{n=1}^{\infty} 3^{- n}\right)}=\color{red}{\left(\frac{1}{2}\right)}$$

Hence,

$$\sum_{n=1}^{\infty} 3^{- n}=\frac{1}{2}$$

**Answer:** $$$\sum_{n=1}^{\infty} 3^{- n}=\frac{1}{2}$$$