3 + frac{5}{1!} + frac{7}{2!} + frac{9}{3!} + | vedclass

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(B) The general term of the series is $T_n = \frac{2n + 1}{(n - 1)!}$ for $n \ge 1$.We can rewrite the general term as $T_n = \frac{2(n - 1) + 3}{(n -

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$5e$

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(B) The general term of the series is $T_n = \frac{2n + 1}{(n - 1)!}$ for $n \ge 1$.We can rewrite the general term as $T_n = \frac{2(n - 1) + 3}{(n - 1)!} = \frac{2(n - 1)}{(n - 1)!} + \frac{3}{(n - 1)!} = \frac{2}{(n - 2)!} + \frac{3}{(n - 1)!}$.The sum of the series is $S = \sum_{n=1}^{\infty} T_n = \sum_{n=1}^{\infty} \frac{2}{(n - 2)!} + \sum_{n=1}^{\infty} \frac{3}{(n - 1)!}$.Note that $\frac{1}{(-1)!} = 0$ and $\frac{1}{0!} = 1$.$S = 2 \left( 0 + \frac{1}{0!} + \frac{1}{1!} + \frac{1}{2!} + \dots \right) + 3 \left( \frac{1}{0!} + \frac{1}{1!} + \frac{1}{2!} + \dots \right)$.$S = 2(e) + 3(e) = 5e$.

$3 + \frac{5}{1!} + \frac{7}{2!} + \frac{9}{3!} + \dots \infty = $

Similar Questions

Which one of the following is not correct for the features of the exponential function given by $f(x) = b^{x}$ where $b > 1$?

$\frac{1}{2!} + \frac{1 + 2}{3!} + \frac{1 + 2 + 3}{4!} + \dots \infty = $

The sum of the series $\sum_{n=1}^{\infty} \frac{n^{2}+6 n+10}{(2 n+1) !}$ is equal to :

The sum of the series $\frac{1^2}{1 \cdot 2!} + \frac{1^2 + 2^2}{2 \cdot 3!} + \frac{1^2 + 2^2 + 3^2}{3 \cdot 4!} + \dots + \frac{1^2 + 2^2 + \dots + n^2}{n(n + 1)!} + \dots \infty$ is equal to:

$\left( {1 + \frac{1}{{2!}} + \frac{1}{{4!}} + \dots} \right) \left( {1 + \frac{1}{{3!}} + \frac{1}{{5!}} + \dots} \right) = $

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