The sum of the series 1 + 1/4 × 2! + 1/16 × 4! + 1/64 × 6! + ad inf. is: - Mathematics MCQ AIEEE 2026 | ExamTest.live

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The sum of the series 1 + \frac{1}{4 \cdot 2 !} + \frac{1}{16 \cdot 4 !} + \frac{1}{64 \cdot 6 !} + \dots ad inf. is:

Solution & Step-by-step Explanation

We know the series expansion: cosh x = \frac{e ^{x} + e ^{- x}}{2} = 1 + \frac{x ^{2}}{2 !} + \frac{x ^{4}}{4 !} + \dots The given series is 1 + \frac{( 1/2 ) ^{2}}{2 !} + \frac{( 1/2 ) ^{4}}{4 !} + \frac{( 1/2 ) ^{6}}{6 !} + \dots This is exactly cosh (1/2) . cosh (1/2) = \frac{e ^{1/2} + e ^{- 1/2}}{2} = \frac{e + 1/ e}{2} = \frac{e + 1}{2 e} .

Try it yourself before checking the explanation above.

The sum of the series 1 + \frac{1}{4 \cdot 2 !} + \frac{1}{16 \cdot 4 !} + \frac{1}{64 \cdot 6 !} + \dots ad inf. is:

\frac{e - 1}{e}

\frac{e + 1}{e}

\frac{e - 1}{2 e}

\frac{e + 1}{2 e}

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