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.

### Instructions

**1.**

The number at the top of the summation symbol is the end (terminus) of the summation. Do you agree?

Set `checkpoint_1`

to `"yes"`

or `"no"`

.

**2.**

What is the approximate sum of

`$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+ \ldots$`

Assign your answer to `checkpoint_2`

in the code editor.