Aspire Faculty ID #14036 · Topic: JAMIA MILLIA ISLAMIA MCA 2019 · Just now
JAMIA MILLIA ISLAMIA MCA 2019

The sum of the series $1 + \dfrac{1}{4 \cdot 2!} + \dfrac{1}{16 \cdot 4!} + \dfrac{1}{64 \cdot 6!} + \cdots$ is:

Solution

Given series = $\displaystyle 1 + \frac{1}{2! \cdot 2^2} + \frac{1}{4! \cdot 2^4} + \frac{1}{6! \cdot 2^6} + \cdots$ This is the expansion of $\dfrac{e^{1/2} + e^{-1/2}}{2} = \dfrac{e^{1/2}(1 + e^{-1})}{2} = \dfrac{e + 1}{2\sqrt{e}}$
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