Series and Sum Calculator with Steps
Calculate series and sums step by step
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.
Your Input
Find $$$\sum_{n=1}^{\infty} 3^{- n}$$$.
Solution
$$$\sum_{n=1}^{\infty} 3^{- n}$$$ 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
$$$\sum_{n=1}^{\infty} 3^{- n} = \frac{1}{2} = 0.5$$$A
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