Question

IS the sum of (3^n - 2^2)/ 2^(2n) convergent and what is the number.
pls show steps.

Answer 1

it converges as :
=(3^n-2^2)/4^n
=3^n/4^n-4/4^n
=(3/4)^n-4^(1-n)
so |3/4|=.75<1 so it converges to zero when it is raised to infinity
and 4^(1-n) when raised to infinity it converges to zero
so the equation converges to zero

Answer 2

thanks can you also find the interval of convergence.