2+2^2 over 3 + 2^3 over 3^2+....... + 2^n+1 over 3^n. Express each sum using summation notation.

Answer 1

The general term is
2^(i+1)/3^i
=2*(2^i)/3^i
=2*(2/3)^i

The summation starts at 2*1, or i=0. The sums expressed in summation notation is therefore:

n
2∑ (2/3)^i
i=0