What is the sum from n=1 to infinity of (n^5)/(6^n) ?

The sum from n=1 to infinity of (n^5)/(6^n) is converges

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sum from n=1 to infinity of (n^5)/(6^n)

n = 1 \sum \infty \frac{n ^{5}}{6 ^{n}}

converges

Solution steps

n = 1 \sum \infty \frac{n ^{5}}{6 ^{n}}

Apply Series Ratio Test:

converges

= converges

k = 0 \sum \infty (\frac{2}{5})^{k}

n = 2 \sum \infty \frac{2}{n ln ( n ^{2} )}

n = 0 \sum \infty 2^{n} + i

n = 1 \sum \infty \frac{1}{ln ( 2 ^{n} )}

n = 1 \sum \infty \frac{3}{9 ^{n + 1}}

What is the sum from n=1 to infinity of (n^5)/(6^n) ?
The sum from n=1 to infinity of (n^5)/(6^n) is converges