What is the sum from n=1 to infinity of 3/(n^5) ?

The sum from n=1 to infinity of 3/(n^5) is converges

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sum from n=1 to infinity of 3/(n^5)

n = 1 \sum \infty \frac{3}{n ^{5}}

converges

Solution steps

n = 1 \sum \infty \frac{3}{n ^{5}}

Apply the constant multiplication rule:

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

= 3 \cdot n = 1 \sum \infty \frac{1}{n ^{5}}

Apply p-Series Test:

converges

= 3 converges

= converges

n = 0 \sum \infty \frac{n ^{2}}{1 + 3 n}

n = 0 \sum \infty (\frac{11}{3})^{n}

n = 1 \sum \infty (1 + c)^{- n}

n = 1 \sum \infty \frac{3}{n ^{2} - 1}

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

What is the sum from n=1 to infinity of 3/(n^5) ?
The sum from n=1 to infinity of 3/(n^5) is converges