Question

Question #7cea5

Answer 1

`9/2`

Explanation:

`sum_(n=0)^oo(1+2^n)/3^n`
`=sum_(n=0)^oo1/3^n+2^n/3^n`
`=sum_(n=0)^oo((1/3)^n+(2/3)^n)`
`=sum_(n=0)^oo(1/3)^n+sum_(n=0)^oo(2/3)^n`

Then, use the sum of the geometric series formula: `sum_(i=0)^ooar^i=a/(1-r),|r|<1` for both sums.

`=1/(1-1/3)+1/(1-2/3)`
`=3/2+3`
`=9/2`