What is the sum from n=1 to infinity of 5/(n^{10)} ?

The sum from n=1 to infinity of 5/(n^{10)} is converges

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sum from n=1 to infinity of 5/(n^{10)}

n = 1 \sum \infty \frac{5}{n ^{10}}

converges

Solution steps

n = 1 \sum \infty \frac{5}{n ^{10}}

Apply the constant multiplication rule:

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

= 5 \cdot n = 1 \sum \infty \frac{1}{n ^{10}}

Apply p-Series Test:

converges

= 5 converges

= converges

n = 0 \sum \infty \frac{7}{2} (- \frac{3}{4})^{n}

n = 1 \sum \infty (0.73)^{n - 1}

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

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

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

What is the sum from n=1 to infinity of 5/(n^{10)} ?
The sum from n=1 to infinity of 5/(n^{10)} is converges