Prove by induction that this expression is a solutionSolutio

Prove by induction that this expression is a solution

Solution

an=(an-1)/3

a0=1

a1=1/3

Suppose it is true for some n = k 1, that is ak=(k-1)/3

Prove that it is true for n = k + 1, that is

ak+1= k/3

ak+a1=k/3

(k-1)/3+1/3=k/3

k/3=k/3

hence proved