A sequence is defined recursively as follows: R(n)= 1 if n=0

R(n)= 5R(n-1)+1 if n >0. While an explicit formula of f(n)= (5^(n+1)-1)/4 for all integers n> or = to 0

Is the hypothesized explicit formula for R(n). In the following steps construct a proof using Mathematical induction that the two are equal for all n> or =0

1. Verify the bases case R(0)= f(0)
2. For k>0 write down the inductive hypothesis for the proof using k as the unspecified integer
3. Complete the proof by writing down the inductive step, that is show that R(k)= f(k)