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

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

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

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

converges

Solution steps

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

Expand

\frac{2 n + 1}{n ^{4}} : \frac{2}{n ^{3}} + \frac{1}{n ^{4}}

= n = 1 \sum \infty \frac{2}{n ^{3}} + \frac{1}{n ^{4}}

Apply the Sum Rule:

\sum a_{n} + b_{n} = \sum a_{n} + \sum b_{n}

= n = 1 \sum \infty \frac{2}{n ^{3}} + n = 1 \sum \infty \frac{1}{n ^{4}}

n = 1 \sum \infty \frac{2}{n ^{3}} =

converges

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

converges

= converges + converges

= converges

\int_{1}^{\infty} (\frac{1}{x ^{2}}) d x

x \to \infty lim (f (x) (x)^{2})

x \to - \infty lim (x^{2} - 1)

(x^{2} + 1) (x^{2} - 2 x)

f (x) = \frac{cos ( x )}{1 - sin ( x )}

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