What is the sum from n=4 to infinity of 1/(n^5) ?

The sum from n=4 to infinity of 1/(n^5) is converges

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sum from n=4 to infinity of 1/(n^5)

n = 4 \sum \infty \frac{1}{n ^{5}}

converges

Solution steps

n = 4 \sum \infty \frac{1}{n ^{5}}

Apply p-Series Test:

converges

= converges

n = 1 \sum \infty (- \frac{5}{8})^{n - 1}

n = 0 \sum \infty e^{- 17 n}

n = 1 \sum \infty 3^{1 - n}

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

n = 1 \sum \infty \frac{1}{4 ^{n}} \cdot 2^{n}

What is the sum from n=4 to infinity of 1/(n^5) ?
The sum from n=4 to infinity of 1/(n^5) is converges