What is the sum from n=1 to infinity of 2/(n^4) ?

The sum from n=1 to infinity of 2/(n^4) is converges

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sum from n=1 to infinity of 2/(n^4)

n = 1 \sum \infty \frac{2}{n ^{4}}

converges

Solution steps

n = 1 \sum \infty \frac{2}{n ^{4}}

Apply the constant multiplication rule:

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

= 2 \cdot n = 1 \sum \infty \frac{1}{n ^{4}}

Apply p-Series Test:

converges

= 2 converges

= converges

n = 1 \sum \infty \frac{2}{n ^{5}}

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

n = 1 \sum \infty (\frac{3}{4})^{- n}

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

n = 1 \sum \infty \frac{2}{n ^{7}}

What is the sum from n=1 to infinity of 2/(n^4) ?
The sum from n=1 to infinity of 2/(n^4) is converges