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

The sum from n=1 to infinity of n!(0)^n is 0

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sum from n=1 to infinity of n!(0)^n

n = 1 \sum \infty n! (0)^{n}

0

Solution steps

n = 1 \sum \infty n! \cdot 0^{n}

Simplify

= n = 1 \sum \infty 0

\sum 0 = 0

= 0

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x \to 7 lim (x^{2})

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What is the sum from n=1 to infinity of n!(0)^n ?
The sum from n=1 to infinity of n!(0)^n is 0