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

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Answer 1 · 2018-05-18T10:52:26

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

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

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

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