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 ! \cdot n}

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

x \to \infty lim (\frac{1}{x ^{\frac{7}{2}}})

y^{3} - (2 x + 2) + 3 x y^{2} y^{^{'}} = 0

\frac{( s + 1 )}{( s + 6 )}

\int \frac{x}{x + y} d x

\frac{d y}{d x}, y^{2} = 12 x

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