# Calculadora de séries e somas com etapas

## Calcular séries e somas passo a passo

Esta calculadora tentará encontrar a soma infinita de séries aritméticas, geométricas, de potência e binomiais, bem como a soma parcial, com etapas mostradas (se possível). Ele também verificará se a série converge.

Sum of:

Variable:

Start Value:

If you need -oo, type -inf.

End Value:

If you need oo, type inf.
If you need a binomial coefficient C(n,k)=((n),(k)), type binomial(n,k).
If you need a factorial n!, type factorial(n).
Variables in the bounds are assumed to be positive.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

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