The sum of the series frac{1}{2!} - frac{1}{3 | vedclass

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(D) We know the expansion of the exponential series: $e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \dots$ Putting $x = -1$ in the

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None of these

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(D) We know the expansion of the exponential series: $e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \dots$ Putting $x = -1$ in the expansion: $e^{-1} = 1 + (-1) + \frac{(-1)^2}{2!} + \frac{(-1)^3}{3!} + \frac{(-1)^4}{4!} + \dots$ $e^{-1} = 1 - 1 + \frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} - \dots$ $e^{-1} = \frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} - \dots$ Thus,the sum of the series is $e^{-1}$ or $\frac{1}{e}$. Since $\frac{1}{e}$ is not among the given options,the correct choice is $(D)$.

The sum of the series $\frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} - \dots$ is

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