The sum of the series 1 + frac{1}{4 cdot 2!} | vedclass

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(B) The expansion of $\cosh(x)$ is given by $\frac{e^x + e^{-x}}{2} = 1 + \frac{x^2}{2!} + \frac{x^4}{4!} + \frac{x^6}{6!} + \dots \infty$. We can rew

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$\frac{e + 1}{2\sqrt{e}}$

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(B) The expansion of $\cosh(x)$ is given by $\frac{e^x + e^{-x}}{2} = 1 + \frac{x^2}{2!} + \frac{x^4}{4!} + \frac{x^6}{6!} + \dots \infty$. We can rewrite the given series as $1 + \frac{(1/2)^2}{2!} + \frac{(1/2)^4}{4!} + \frac{(1/2)^6}{6!} + \dots \infty$. By comparing this with the expansion of $\cosh(x)$,we set $x = \frac{1}{2}$. Thus,the sum is $\frac{e^{1/2} + e^{-1/2}}{2} = \frac{\sqrt{e} + \frac{1}{\sqrt{e}}}{2} = \frac{e + 1}{2\sqrt{e}}$.

The sum of the series $1 + \frac{1}{4 \cdot 2!} + \frac{1}{16 \cdot 4!} + \frac{1}{64 \cdot 6!} + \dots$ to infinity is

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