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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

n = 0 \sum \infty e^{- 0.2 n}

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

n = 0 \sum \infty 2 (\frac{1}{5})^{n + 1}

k = 1 \sum \infty \frac{1}{k ( k + 2 )}

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

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