Use mathematical induction to prove the formula for every positive integern.

4(1+5+5²+5³++5ⁿ¹) =5ⁿ1

FindS₁

whenn= 1.

S₁

=

Assume that

S_k=4(1+5+5²+5³++5^k1) =5^k1

.

Then,

S_k+1=S_k+a_{k+ 1}= [4(1+5+5²+5³++5^k1)] +a_{k+ 1}.

a_{k+ 1}=

Use the equation fora_{k+ 1}andS_k

to find the equation forS_{k+ 1}.

S_{k+ 1}

=