Question

How do you find the sum of `(1+1)+(1/3+1/5)+(1/9+1/25)+...+(3^-n+5^-n)+...`?

Answer 1

`sum_(n=0)^oo (3^(-n)+5^(-n)) =11/4`

Explanation:

We have:

`sum_(n=0)^oo (3^(-n)+5^(-n)) = sum_(n=0)^oo (1/3)^n + sum_(n=0)^oo (1/5)^n`

Both these series are geometric series so the sum is:

`sum_(n=0)^oo (3^(-n)+5^(-n)) = 1/(1-1/3) + 1/(1-1/5) =3/2+5/4=11/4`