What is the sum from n=1 to infinity of 5/(n^4) ?

The sum from n=1 to infinity of 5/(n^4) is converges

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sum from n=1 to infinity of 5/(n^4)

n = 1 \sum \infty \frac{5}{n ^{4}}

converges

Solution steps

n = 1 \sum \infty \frac{5}{n ^{4}}

Apply the constant multiplication rule:

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

= 5 \cdot n = 1 \sum \infty \frac{1}{n ^{4}}

Apply p-Series Test:

converges

= 5 converges

= converges

x \to \infty lim (\frac{x}{3 x})

\frac{d ^{2}}{d x ^{2}} (\frac{1}{4 x ^{2} + 5 x})

\frac{d}{d x} (cos (7 - 2 x))

\frac{d}{d x} (e^{x} (x \cdot sin (x) + (1 - x) \cdot cos (x)))

\frac{\partial}{\partial x} (\frac{1}{x ^{7}})

What is the sum from n=1 to infinity of 5/(n^4) ?
The sum from n=1 to infinity of 5/(n^4) is converges