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

Question 43

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Find an infinite series that converges to the value of ∫012xe−x\int _ { 0 } ^ { 1 } 2 x e ^ { - x } dx. Is 1−23+14−115…1 - \frac { 2 } { 3 } + \frac { 1 } { 4 } - \frac { 1 } { 15 } \ldots correct?

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