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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

f (x) = x^{2} + 3, at x = - 1

f (x) = (3 x^{6} + 2 x^{3})^{4}

\frac{d y}{d x} = y (3 y - 6)

\frac{d}{d x} (\frac{1}{3 x ^{4} + 1})

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