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

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

Prove by the principle of mathematical induction that 1+4+7+…..+(3n-2)=1/2n(3n-1),AA n in N .

Prove by the principle of mathematical induction that 4+8+12+….+4n=2n(n+1),AA n in N .

Prove by the principle of mathematical induction that 2+5+8+11+….+(3n-1)=1/2n(3n+1),AA n in N .

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 for all n in N. 3^(2n)+7 is divisible by 8 for all n in N .

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