Prove by mathematical induction `2^(3n)-1` is divisible by 7.

(n^2-1) is divisible by 8,if n is

Prove by the principle of mathematical induction that for all n in N. (2^(3n)-1) is divisible by 7 for all n in N .

Prove by mathematical induction for all n in N that 1/2+1/4+1/8+…..+1/2^n=1-1/2^n.

Prove by the principle of mathematical induction that for all n in N. 5^(2n)-1 is divisible by 24 for all n in N .

Prove that: 33! is divisible by 2^15 .

Prove by the principle of mathematical induction that for all n in N. 3^(2n)+7 is divisible by 8 for all n in N .

Prove by the principle of mathematical induction that for all n in N. (10^(2n-1)+1) is divisible by 11 for all n in N .

Prove by the principle of mathematical induction that for all n in N. Sn=n^3+3n^2+5n+3 is divisible by 3 for all n in N

For any natural number n prove by mathematical induction that: 1.2+2.3+3.4+…..+n(n+1)=1/3n(n+1)(n+2) .

Prove by the principle of mathematical induction that 1+2+2^2+….2^(n-1)=2^n-1,AA n in N .