What is the sum from n=0 to infinity of (4^n)/(n!) ?

The sum from n=0 to infinity of (4^n)/(n!) is converges

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sum from n=0 to infinity of (4^n)/(n!)

n = 0 \sum \infty \frac{4 ^{n}}{n !}

converges

Solution steps

n = 0 \sum \infty \frac{4 ^{n}}{n !}

Apply Series Ratio Test:

converges

= converges

x \to \infty lim (1. 1^{x})

x \to 1 lim (x^{4} - 3 x^{2} + 6)

x \to - 1 lim (\frac{x ^{3} + x}{1 + x})

\frac{\partial}{\partial x} (x \cdot y \cdot cos (3 x) + e^{x y})

x \to 0 lim (\frac{x - 12}{x - 4})

What is the sum from n=0 to infinity of (4^n)/(n!) ?
The sum from n=0 to infinity of (4^n)/(n!) is converges