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

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

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 .

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 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 for all n in N. (10^(2n-1)+1) is divisible by 11 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. (2^(3n)-1) is divisible by 7 for all n in N .

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