Summing an infinite series question

[TheRascalKing]

Homework Statement

I need to fin the sum of the following two infinite series:
1. Ʃ[n=0 to ∞] ((2^n + 3^n)/6^n)

and 2. Ʃ[n=2 to ∞] (2^n + (3^n / n^2)) (1/3^n)

Homework Equations

use the sum Ʃ[n=2 to ∞] (1/n^2) = ∏^2 / 6 as necessary

The Attempt at a Solution

I tried to manipulate them both to make them geometric or telescoping, to no avail. It seems like neither series is telescoping or geometric, so isn't it impossible to definitively sum them?

I started to sum them by adding their partial sums, but they converge very slowly and it would take hundreds of calculations to provide enough evidence for the sums.

 

[Curious3141]

Hint:

1. Split them into two rational expressions. Simplify (ask what is $\frac{a^n}{b^n}$?)

2. Multiply the bracket out. Simplify.

It's all just algebra.