What is the sum from n=1 to infinity of (n^4)/(9^n) ?

The sum from n=1 to infinity of (n^4)/(9^n) is converges

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sum from n=1 to infinity of (n^4)/(9^n)

n = 1 \sum \infty \frac{n ^{4}}{9 ^{n}}

converges

Solution steps

n = 1 \sum \infty \frac{n ^{4}}{9 ^{n}}

Apply Series Ratio Test:

converges

= converges

n = 1 \sum \infty \frac{2 + sin ( n )}{n}

n = 2 \sum \infty (\frac{2}{7})^{2 n}

n = 1 \sum \infty 2 (0.7)^{n - 1}

n = 0 \sum \infty cos (n) π

n = 1 \sum \infty \frac{1}{3 ^{n} n !}

What is the sum from n=1 to infinity of (n^4)/(9^n) ?
The sum from n=1 to infinity of (n^4)/(9^n) is converges