Prove by Induction question, 2+6+18+...+ 2.3^n-1 = (3^n)-1

Question

Can anyone help me solving this problem, Im really really lost. Thank you

Answer 1

For k=1

2=3¹-1=2 (true)

Assume that this is true for k=n and show that it is true for k=n+1 as well

2+2*3+2*3²+...+2*3^n-1+2*3ⁿ =3ⁿ-1+2*3ⁿ

=3ⁿ(1+2)-1=3^n*3¹-1=3ⁿ⁺¹-1. Q.E.D