Question

Which of the following can be used to evaluate the series 9 k=1 2(4) k=1?

Answer 1

Option (3)

Explanation:

Given expression represents the sum of k terms of a geometric sequence.

`\sum_(k=1)^(9)2(4)^(k-1)`

Since, formula to calculate the sum of a geometric sequence is given by,

`\sum_(n=1)^(n)a(r)^(n-1)=(a(1-r^n))/(1-r)`

By this formula,sum of 9 terms of the given sequence will be,

`\sum_(k=1)^(9)2(4)^(k-1)=(2(1-4^9))/(1-4)`

Therefore, Option (3) will be the answer.