A calculus problem by Kumar Mayank

Calculus Level 1

$\dfrac12 - \dfrac16 + \dfrac1{24} - \dfrac1{120} + \cdots = \, ?$

Note that $$6 = 2\times 3, 24 = 2\times3\times4, 120 = 2\times3\times4\times5, \cdots$$.

 Clarification: $$e$$ denotes Euler's number, $$e \approx 2.71828$$.

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