Question:medium
The value of
\[
\sum_{k=1}^{\infty} (-1)^{k+1}\left(\frac{k(k+1)}{k!}\right)
\]
is:
The value of
\[
\sum_{k=1}^{\infty} (-1)^{k+1}\left(\frac{k(k+1)}{k!}\right)
\]
is:
Show Hint
Always try to rewrite factorial expressions to resemble the series of \( e^x \), \( xe^x \), or their derivatives.
Updated On: Mar 29, 2026
- \( \dfrac{1}{e} \)
- \( \dfrac{2}{e} \)
- \( \sqrt{e} \)
- \( \dfrac{e}{2} \)
Show Solution
The Correct Option is B
Solution and Explanation
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