JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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The sum of the series

\frac{1^2}{1 \cdot 2 !}+\frac{1^2+2^2}{2 \cdot 3 !}+\frac{1^2+2^2+3^2}{3 \cdot 4 !}+\ldots+\frac{1^2+2^2+\ldots+n^2}{n \cdot(n+1) !}+\ldots \infty

: Equals

View answer and explanation

Correct option: C

\frac{3 e-1}{6}

Option C ((3e-1)/6) is correct because the sum of the given infinite series can be simplified and expressed in terms of the exponential constant 'e'.

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