Sum 2^2n 3^1-n,, n from 1 to infinity

Answer 1

First start by rewriting it as the sum of 2²ⁿ*3¹*3^-n.

Now we can rewrite this as

Sum of 3* (4ⁿ/3ⁿ)

Which is the same as Sum of 3*(4/3)ⁿ which is in the form of a geometric series with |r|> 1, so it diverges.