Prove that summation(0 to infinity) n^2/n!=2e

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1 + 2 (1 - \frac{1}{n}) + 3 {(1 - \frac{1}{n})}^{2} + . . .

n \in N

n^{2}

1 + 2 (1 - \frac{1}{n}) + 3 (1 - \frac{1}{n})^{2} + . . . .

a_{n^{2} + 1} = (n^{2} + 1^{2}) - (n^{2} + 1) + 1 = (n^{2} + n + 1) (n^{2} - n + 1) =

1 + 2 (1 - \frac{1}{n}) + 3 {(1 - \frac{1}{n})}^{2} + . . .

1 + 2 (1 - \frac{1}{n}) + 3 {(1 - \frac{1}{n})}^{2} + . . .

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