Find the sum of the finite geometric sequence of sum^100_i=1 15(2/3)^i−1

Marilyn Cameron

Marilyn Cameron

Answered question

2022-10-14

Find the sum of the finite geometric sequence of i = 1 100 15 ( 2 3 ) i - 1

Answer & Explanation

Kyle Delacruz

Kyle Delacruz

Beginner2022-10-15Added 21 answers

To find the sum k = 0 n a 0 r n of a geometric series with first term a 0 and ratio r, we use the following formula
k = 0 n a 0 r n = a 0 ( 1 - r n ) 1 - r
So, if k = i - 1 , then
i = 1 100 15 ( 2 3 ) i - 1 = 15 k = 0 99 ( 2 3 ) k = 15 ( 1 ( 1 - ( 2 3 ) 99 ) 1 - 2 3 ) = 45

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