Find an infinite series that converges to the value of $\int _ { 0 } ^ { 1 } 2 x e ^ { - x }$ dx. Is $1 - \frac { 2 } { 3 } + \frac { 1 } { 4 } - \frac { 1 } { 15 } \ldots$ correct?

Question

Quizplus · Accepted Answer

The given series is the Taylor series expansion of the function $2xe^{-x}$ around $x=0$. Since the Taylor series converges to the function it represents, the given series converges to the value of the integral.

Find an Infinite Series That Converges to the Value Of \int