What is the sum from n=1 to infinity of 5/(n^9) ?

The sum from n=1 to infinity of 5/(n^9) is converges

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sum from n=1 to infinity of 5/(n^9)

n = 1 \sum \infty \frac{5}{n ^{9}}

converges

Solution steps

n = 1 \sum \infty \frac{5}{n ^{9}}

Apply the constant multiplication rule:

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

= 5 \cdot n = 1 \sum \infty \frac{1}{n ^{9}}

Apply p-Series Test:

converges

= 5 converges

= converges

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

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

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

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

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

What is the sum from n=1 to infinity of 5/(n^9) ?
The sum from n=1 to infinity of 5/(n^9) is converges