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

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

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

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

converges

Solution steps

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

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

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

Apply p-Series Test:

converges

= 5 converges

= converges

\frac{d}{d x} (\frac{1}{x ^{4}} + \frac{1}{x ^{8}})

\frac{d}{d x} (\frac{x ^{3}}{3} - \frac{3}{x ^{3}})

\int \frac{x}{x ^{2} - x - 1} d x

\frac{\partial}{\partial x} (2 x + 3 y - 7)

f (x) = \frac{x ^{2} - 36}{x - 6}

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