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}

Simplify

(\frac{2}{n})^{4} : \frac{16}{n ^{4}}

= n = 1 \sum \infty \frac{16}{n ^{4}}

Apply the constant multiplication rule:

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

= 16 \cdot n = 1 \sum \infty \frac{1}{n ^{4}}

Apply p-Series Test:

converges

= 16 converges

= converges

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