What is the sum from n=1 to infinity of 1/(3n^5+4) ?

The sum from n=1 to infinity of 1/(3n^5+4) is converges

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sum from n=1 to infinity of 1/(3n^5+4)

n = 1 \sum \infty \frac{1}{3 n ^{5} + 4}

converges

Solution steps

n = 1 \sum \infty \frac{1}{3 n ^{5} + 4}

Apply Series Comparison Test:

converges

= converges

n = 0 \sum \infty \frac{i ^{2 n}}{3 n}

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

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

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

n = 0 \sum \infty (\frac{1}{2})^{2}

What is the sum from n=1 to infinity of 1/(3n^5+4) ?
The sum from n=1 to infinity of 1/(3n^5+4) is converges