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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

\int t^{- 2} e^{t} d t

(- 5, 2), (5, - 4)

\frac{d y}{d x} - \frac{x}{y} = 2 y

ln (1 + 4^{x})

\frac{d y}{d x} = x^{7} - \frac{1}{x ^{7}}

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