Sum((19/20)^n, (n, 0, oo))

La calculadora intentará encontrar la suma $$$\sum_{n=0}^{\infty} \left(\frac{19}{20}\right)^{n}$$$ o indicar si es convergente, mostrando los pasos.

Sumando:

Variable:

Deje en blanco para la detección automática.

Valor inicial:

Valor final:

If you need a binomial coefficient $$$C(n,k) = {\binom{n}{k}}$$$, type binomial(n,k).
If you need a factorial $$$n!$$$, type factorial(n).

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Tu entrada

Halla $$$\sum_{n=0}^{\infty} \left(\frac{19}{20}\right)^{n}$$$.

Solución

$$$\sum_{n=0}^{\infty} \left(\frac{19}{20}\right)^{n}$$$ is an infinite geometric series with the first term $$$b=1$$$ and the common ratio $$$q=\frac{19}{20}$$$.

By the ratio test, it is convergent.

Its sum is $$$S=\frac{b}{1-q}=20$$$.

Therefore,

$${\color{red}{\left(\sum_{n=0}^{\infty} \left(\frac{19}{20}\right)^{n}\right)}}={\color{red}{\left(20\right)}}$$

Hence,

$$\sum_{n=0}^{\infty} \left(\frac{19}{20}\right)^{n}=20$$

Respuesta

$$$\sum_{n=0}^{\infty} \left(\frac{19}{20}\right)^{n} = 20$$$A

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