What is the sum from n=1 to infinity of 3/(n^{10)} ?

The sum from n=1 to infinity of 3/(n^{10)} is converges

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sum from n=1 to infinity of 3/(n^{10)}

n = 1 \sum \infty \frac{3}{n ^{10}}

converges

Solution steps

n = 1 \sum \infty \frac{3}{n ^{10}}

Apply the constant multiplication rule:

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

= 3 \cdot n = 1 \sum \infty \frac{1}{n ^{10}}

Apply p-Series Test:

converges

= 3 converges

= converges

k = 2 \sum \infty (- 0.1)^{k}

k = 1 \sum \infty 3 k e^{- k}

n = 1 \sum \infty \frac{7}{e ^{n}}

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

n = 1 \sum \infty \frac{6 ^{n}}{n ^{3}}

What is the sum from n=1 to infinity of 3/(n^{10)} ?
The sum from n=1 to infinity of 3/(n^{10)} is converges