Question

How do you find the sum of the geometric series `8+4+2+1+…`?

Answer 1

The sum of a convergent geometric series `sum_{n=0}^{infty}ar^n` is `frac{a}{1-r}`. Since `a=8` and `r=1/2` in the posted geometric series, the sum is `frac{8}{1-frac{1}{2}}=16`.