Given that sum from n=1 to infinity ( 3^n + 2^n) / 6^n.
Was asked to determine if it's convergent or divergent. If convergent, find its sum.
What i did was
(3/6)^n + (2/6)^n
= (1/2)^n + (1/3)^n
since both 1/2 and 1/3 are less than 1. so it's convergent.
hence I used a/1-r to find the sum to infinity for both 1/2 and 1/3 seperate cases and added up both the sum. But it was wrong. why?