Calculadora de séries e somas com etapas

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.

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

Calculadora de séries e somas com etapas

Calcular séries e somas passo a passo

Answer