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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

n = 0 \sum \infty \frac{n}{ln ( n )}

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

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

n = 1 \sum \infty \frac{n}{n !}

n = 2 \sum \infty (0.33)^{n}

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