Question

HELP PLEASE NOW I NEED HELP!

Answer 1

18

Explanation:

the expression inside the ∑ is the nth term of a geometric sequence , that is

`a_(n)` = a₁
`(r)^(n-1)`

where a₁ is the first term and r the common ratio

6
`((2)/(3)) ^(n-1)` ← is in this form with

a₁ = 6 and r =
`(2)/(3)`

the upper value of the ∑ is ∞

the sum to infinity of a geometric sequence is

S∞ =
`(a_(1) )/(1-r)` : | r | < 1 , then using the values a₁ = 6 and r =
`(2)/(3)`

S∞ =
`(6)/(1-(2)/(3) )` =
`(6)/((1)/(3) )` = 6 ×
`(3)/(1)` = 18