We introduce summation notation in detail, a method for providing a compact description of a summation. Summations start somewhere specific and either terminate definitively (finite) or continue without bounds (infinite). Summations often have terms called “variables,” and may also have constants. Summations that only compute part of a sequence are called “partial sums.” For example:

$\sum\limits_{i=1}^{n}5i$

If we limit n to 5, then we have

$\sum\limits_{i=1}^{5}5i=5+10+15+20+25=75$

We already saw that the inverse factorial yields an approximation to e.

$\sum\limits_{i=1}^{n}\frac{1}{n!}\approx e$

Although we have a summation formula, e will be valid to only the fourth decimal place, even with n = 100,000.