Find the sum to infinity of the series frac{1 | vedclass

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(B) We know the expansion of $e^x$ is given by:$e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \dots + \infty$Substitute $x = -1$ in

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$e^{-1}$

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(B) We know the expansion of $e^x$ is given by:$e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \dots + \infty$Substitute $x = -1$ into 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} = 0 + \frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} - \dots$Therefore,the sum of the series $\frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} - \dots$ is $e^{-1}$.

Find the sum to infinity of the series $\frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} - \dots$

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