What is the sum from n=0 to infinity of (1+n)/(n!) ?

The sum from n=0 to infinity of (1+n)/(n!) is converges

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sum from n=0 to infinity of (1+n)/(n!)

n = 0 \sum \infty \frac{1 + n}{n !}

converges

Solution steps

n = 0 \sum \infty \frac{1 + n}{n !}

Apply Series Ratio Test:

converges

= converges

n = 2 \sum \infty \frac{3 ^{n}}{n !}

n = 1 \sum \infty \frac{8}{n + 2} - \frac{8}{n}

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

n = 1 \sum \infty 6^{- n}

k = 2 \sum \infty (- 0.45)^{k}

What is the sum from n=0 to infinity of (1+n)/(n!) ?
The sum from n=0 to infinity of (1+n)/(n!) is converges