Question

What is the sum of the geometric series?

Answer 1

Essentially this is asking you to sum the first three values of the geometric series that starts with i being 1 and has the rule of (
`8((1)/(4))^(i-1)`).

Since we must sum the first three geometric values we need to see what the value of i will be for the first three. The sigma notation shows us that the first i will be equal to 1. This means the second i is 2 and the third i is 3.

Knowing this you can plug in the corresponding i values into (
`8((1)/(4))^(i-1)`) and sum it all together

(
`8((1)/(4))^(1-1)`) + (
`8((1)/(4))^(2-1)`) + (
`8((1)/(4))^(3-1)`)

(
`8((1)/(4))^(0)`) + (
`8((1)/(4))^(1)`) + (
`8((1)/(4))^(2)`)

(
`8(1)`) + (
`8((1)/(4))`) + (
`8((1)/(16))`)

(8) + (2) + (
`(1)/(2))`)

10 +
`(1)/(2))`

`(21)/(2))`

10.5

Hope this helped!

~Just a girl in love with Shawn Mendes