What is the sum from n=1 to infinity of (15n!)/(n^n) ?

The sum from n=1 to infinity of (15n!)/(n^n) is converges

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sum from n=1 to infinity of (15n!)/(n^n)

n = 1 \sum \infty \frac{15 n !}{n ^{n}}

converges

Solution steps

n = 1 \sum \infty \frac{15 n !}{n ^{n}}

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

= 15 \cdot n = 1 \sum \infty \frac{n !}{n ^{n}}

Apply Series Ratio Test:

converges

= 15 converges

= converges

\frac{\partial}{\partial x} (2 x + 3 y + 6 x y e^{3 x^{2} y})

\frac{\partial}{\partial x} (x^{2} + x e^{2 y})

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

x = 0, y = x^{2}, y = x + 2

x \to - 1 lim (- 6)

What is the sum from n=1 to infinity of (15n!)/(n^n) ?
The sum from n=1 to infinity of (15n!)/(n^n) is converges