What is the sum from n=0 to infinity of (2n-1)/(n!) ?

The sum from n=0 to infinity of (2n-1)/(n!) is converges

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sum from n=0 to infinity of (2n-1)/(n!)

n = 0 \sum \infty \frac{2 n - 1}{n !}

converges

Solution steps

n = 0 \sum \infty \frac{2 n - 1}{n !}

Expand

\frac{2 n - 1}{n !} : \frac{2 n}{n !} - \frac{1}{n !}

= n = 0 \sum \infty \frac{2 n}{n !} - \frac{1}{n !}

Apply the Sum Rule:

\sum a_{n} + b_{n} = \sum a_{n} + \sum b_{n}

= n = 0 \sum \infty \frac{2 n}{n !} - n = 0 \sum \infty \frac{1}{n !}

n = 0 \sum \infty \frac{2 n}{n !} =

converges

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

converges

= converges - converges

= converges

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\frac{d}{d x} 9 x^{2} y^{2} = 1

\int (tan (x) + sec (x)) d x

What is the sum from n=0 to infinity of (2n-1)/(n!) ?
The sum from n=0 to infinity of (2n-1)/(n!) is converges