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.
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.
$\frac{16004}{315}.$ 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 $n\to\infty$.