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

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 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. 5^(2n)-1 is divisible by 24 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

Prove by the principle of mathematical induction that 2+4+6+8+…..2n=n(n+1)

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) .

By mathematical induction prove that 1+3+5+7+…..+(2n-1)=n^2

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 1+4+7+…..+(3n-2)=1/2n(3n-1),AA n in N .