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 !}

Apply Series Ratio Test:

converges

= converges

- 2 e^{x + 2} + e^{- 5}

y^{^{'}} = \frac{4 x ^{5} e ^{\frac{y}{x}} + x ^{3} y ^{2}}{x ^{4} y}

\int e^{2 x} cos (x) d x

\frac{d}{d x} (sin^{n} (x) cos (n) x)

\frac{d ^{2}}{d x ^{2}} (\frac{x}{1 + x ^{2}})

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