What is the sum from n=0 to infinity of (n^5)/(3^n) ?

The sum from n=0 to infinity of (n^5)/(3^n) is converges

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sum from n=0 to infinity of (n^5)/(3^n)

n = 0 \sum \infty \frac{n ^{5}}{3 ^{n}}

converges

Solution steps

n = 0 \sum \infty \frac{n ^{5}}{3 ^{n}}

Apply Series Ratio Test:

converges

= converges

n = 0 \sum \infty 0^{n}

n = 2 \sum \infty \frac{3}{( - 5 ) ^{n}}

n = 2 \sum \infty \frac{1}{n ^{2} + 2 n}

n = 1 \sum \infty \frac{2}{n ^{0.85}}

n = 1 \sum \infty (- \frac{6}{7})^{n - 1}

What is the sum from n=0 to infinity of (n^5)/(3^n) ?
The sum from n=0 to infinity of (n^5)/(3^n) is converges