Question

How do you find the sum of the finite geometric sequence of `sum_(i=1)^100 15(2/3)^(i-1)`?

Answer 1

`sum_(i=1)^100 15(2/3)^(i-1)=`

Explanation:

To find the sum `sum_(k=0)^na_0r^n` of a geometric series with first term `a_0` and ratio `r`, we use the following formula

`sum_(k=0)^na_0r^n=(a_0(1-r^n))/(1-r)`

So, if `k=i-1`, then

`sum_(i=1)^100 15(2/3)^(i-1)=15sum_(k=0)^99 (2/3)^(k)=15((1(1-(2/3)^99))/(1-2/3))=45`