Use mathematical induction to prove the following statement: 8"-1 is a multiple of 7 for all nen

with Step-by-step explanation:

We are given that

P(n)=

We have to prove that given statement is a multiple of 7 using mathematical induction for all natural numbers n belongs to N.

Suppose n=1

Then P(1)=8-1=7

Hence, it is a multiple of 7 .Therefore, it is true for n=1

We suppose that it is true for n=k

Then P(k)= is a multiple of 7.

We shall prove that it is true for n=k+1

P(k+1)= is a multiple of 7

LHS=

=

=

=

=  because is a multiple of 7 therefore

=

P(k+1) is a multiple of 7.

Therefore, P(n) is true for all natural numbers belongs to N.

step-by-step explanation: