What is the sum from n=0 to infinity of (-1)^n((ln(2))^n)/(n!) ?

The sum from n=0 to infinity of (-1)^n((ln(2))^n)/(n!) is converges

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sum from n=0 to infinity of (-1)^n((ln(2))^n)/(n!)

n = 0 \sum \infty (- 1)^{n} \frac{( ln ( 2 ) ) ^{n}}{n !}

converges

Solution steps

n = 0 \sum \infty (- 1)^{n} \frac{( ln ( 2 ) ) ^{n}}{n !}

Apply Alternating Series Test:

converges

= converges

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What is the sum from n=0 to infinity of (-1)^n((ln(2))^n)/(n!) ?
The sum from n=0 to infinity of (-1)^n((ln(2))^n)/(n!) is converges