The value of k = 1 ( - 1 ) k + 1 ( k ( k + 1 ) k ) is [2026]

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Solution

Q.
The value of $\sum_{k = 1}^{\infty} {(- 1)}^{k + 1} ((\frac{k (k + 1)}{k!}))$ is [2026]

1 $\frac{1}{e}$

2 $\frac{e}{2}$

3 $\sqrt{e}$

4 $\frac{2}{e}$

Ans.
(1)

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