Prove by the principle of mathematical induction that for all `n in N` : `1+4+7++(3n-2)=1/2n(3n-1)`

Prove by the principle of mathematical induction that for all n in N:1+4+7+...+(3n-2)=(1)/(2)n(3n-1)

Prove by the principle of mathematical induction that for all n belongs to N :\ 1/(1. 3)+1/(3.5)+1/(5.7)++1/((2n-1)(2n+1))=n/(2n+1)

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 !=psi lon N;n1+3+3^(2)+......+3^(n-1)=(3^(n)-1)/(2)

Prove that by using the principle of mathematical induction for all n in N : (2n+7) lt (n+3)^(2)

Prove that by using the principle of mathematical induction for all n in N : (2n+7) lt (n+3)^(2)

Prove that by using the principle of mathematical induction for all n in N : (2n+7) lt (n+3)^(2)

Prove the following by using the principle of mathematical induction for all n in N :- 1 +3 + 3^2 +....+3^(n-1)=((3^n-1))/2 .

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