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What is the value of the summation $\sum_{x = 1}^7 \frac{4^x}{x!}$

I know that it has something to do with $e^x$, but that only happens when $x$ is from - to infinite. Thanks for the help.

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    That $x$ in the summation makes my hands itch.2011-10-10

1 Answers 1

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$\frac{16004}{315}.$ And what?

Edit The OP wrote in a comment:

I am looking for a more general way of doing this if it exists so I can do it for larger values.

In this context (which is not the same as the context of the question), one might mention that, for every $n\geqslant3$, $ \mathrm e^4-1-r_{n+1}u_n\leqslant\sum_{x=1}^n\frac{4^x}{x!}\leqslant\mathrm e^4-1-r_{n+1}v_n, $ with $ r_n=\frac{4^{n}}{n!},\quad u_n=\frac{n+2}{n-2},\quad v_n=1, $ and that $u_n\to1$, $v_n\to1$ and $r_n\to0$ when $n\to\infty$.