Question

How do you find the sum of the finite geometric sequence of `Sigma 2(-1/4)^n` from n=0 to 40?

Answer 1

`(8/5)*(1+(1/4)^41)`
`~=1.60000000...`

Explanation:

There are 41 terms in the series. The common ratio, `r` is `-(1/4)` and the first term, `a` is `2(-1/4)60` which is `2`. Therefore the sum of the first 41 terms is `a*(1-r^n)/(1-r)`
`=2*(1-(-1/4)^41)/(1-(-1/4))`
`=8/5*(1+(1/4)^41)` because 41 is odd
`~=1.6`
because `(1/4)^41` is negligible