i-0-0-5x-2-i-i-integrate-

Question Number 148809 by jlewis last updated on 31/Jul/21

\underset{i = 0}{\sum^{\infty}} [(- 0 . {5 x}^{2}) i / i!] integrate

Answered by qaz last updated on 31/Jul/21

\underset{n = 0}{\sum^{\infty}} \frac{- \frac{1}{2} x^{2} n}{n!}

= - \frac{1}{2} x^{2} (yD) ∣_{y = 1} \underset{n = 0}{\sum^{\infty}} \frac{y^{n}}{n!}

= - \frac{1}{2} x^{2} ({ye}^{y}) ∣_{y = 1}

= - \frac{e}{2} x^{2}

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