Question

Which of the following can be used to evaluate the series

Answer 1

`5((1-((2)/(3) )^8)/(1-(2)/(3) ))`

Explanation:

The given series is
`\sum_(k=1)^85((2)/(3))^(k-1)`

We want to write an expression that can be used to evaluate this series.

Since this is a geometric series, we use the formula for the sum of the first k terms.

`S_k=a((1-r^k)/(1-r))`

From the given series the first term is
`a=5` and the common ratio is
`r=(2)/(5)` and k=8

We substitute the values to obtain:

`S_8=5((1-((2)/(3) )^8)/(1-(2)/(3) ))`