• 1+3+3^2+...+(3^n-1)=(3^n)-1/2

1 + 3 + 3² + 3³ + ......+ 3^n-1

It's a GP, with first term a = 1, common ratio r = 3

The Sum of GP to n terms is a[rⁿ - 1]/ [r - 1]

1[3ⁿ - 1]/[3 - 1]

= (3ⁿ - 1)/2