Question

How do I find the sum of the geometric series 8 + 4 + 2 + 1?

Answer 1

Now, this is called a finite sum, because there are a countable set of terms to be added. The first term, `a_1=8` and the common ratio is `1/2` or .5. The sum is calculated by finding: `S_n= frac{a_1(1-R^n)}{(1-r)` = `frac{8(1-(1/2)^4)}\(1-1/2)` = `frac{8(1-1/16)}{1-(1/2)}` =`8frac{(15/16)}{1/2}` = `(8/1)(15/16)(2/1)` = 15.

It is interesting to note that the formula works the opposite way, too:
`(a_1(r^n-1))/(r-1)`. Try it on a different problem!