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

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

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

x = 0 \sum \infty \frac{1}{x !}

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

n = 4 \sum \infty \frac{2}{n ( n - 1 )}

n = 1 \sum \infty \frac{n}{n ^{2} + 7}

n = 0 \sum \infty \frac{1}{n \cdot 3 ^{n}}

n = 0 \sum \infty 7

n = 0 \sum \infty - 3 + 4 n^{5}

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