The sum of the series 1 + frac{3}{2!} + frac{ | vedclass

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(D) The general term of the series is $T_n = \frac{2^n - 1}{n!}$ for $n \ge 1$.The sum $S = \sum_{n=1}^{\infty} \frac{2^n - 1}{n!}$.$S = \sum_{n=1}^{\

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$e(e - 1)$

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(D) The general term of the series is $T_n = \frac{2^n - 1}{n!}$ for $n \ge 1$.The sum $S = \sum_{n=1}^{\infty} \frac{2^n - 1}{n!}$.$S = \sum_{n=1}^{\infty} \frac{2^n}{n!} - \sum_{n=1}^{\infty} \frac{1}{n!}$.Recall the expansion $e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!} = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \dots$.Thus,$\sum_{n=1}^{\infty} \frac{2^n}{n!} = (e^2 - 1)$ and $\sum_{n=1}^{\infty} \frac{1}{n!} = (e - 1)$.$S = (e^2 - 1) - (e - 1) = e^2 - e = e(e - 1)$.

The sum of the series $1 + \frac{3}{2!} + \frac{7}{3!} + \frac{15}{4!} + \dots \text{to } \infty$ is

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