Find the sum of the series frac{1}{2!} + frac | vedclass

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(B) We know the expansion of $\cosh(x) = \frac{e^x + e^{-x}}{2} = 1 + \frac{x^2}{2!} + \frac{x^4}{4!} + \frac{x^6}{6!} + \dots \infty$. Setting $x = 1

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$\frac{(e - 1)^2}{2e}$

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(B) We know the expansion of $\cosh(x) = \frac{e^x + e^{-x}}{2} = 1 + \frac{x^2}{2!} + \frac{x^4}{4!} + \frac{x^6}{6!} + \dots \infty$. Setting $x = 1$,we get: $\frac{e^1 + e^{-1}}{2} = 1 + \frac{1}{2!} + \frac{1}{4!} + \frac{1}{6!} + \dots \infty$. $\frac{1}{2} \left( e + \frac{1}{e} \right) = 1 + \frac{1}{2!} + \frac{1}{4!} + \frac{1}{6!} + \dots \infty$. Therefore,$\frac{1}{2!} + \frac{1}{4!} + \frac{1}{6!} + \dots \infty = \frac{1}{2} \left( \frac{e^2 + 1}{e} \right) - 1$. $= \frac{e^2 + 1 - 2e}{2e} = \frac{(e - 1)^2}{2e}$.

Find the sum of the series $\frac{1}{2!} + \frac{1}{4!} + \frac{1}{6!} + \dots \infty$.

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