[" Prove by the principle of induction that for all "n in N],[2+5+8+11+......+(3n-1)=(n(3n+1))/(2)]

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 induction that for all n N ,\ (10^(2n-1)+1) is divisible by 11.

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 !=psi lon N;n1+3+3^(2)+......+3^(n-1)=(3^(n)-1)/(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. (2^(3n)-1) is divisible by 7 for all n in N .

Prove that by using the principle of mathematical induction for all n in N : 1.3+3.5+5.7+....+(2n-1)(2n+1)= (n(4n^(2)+6n-1))/(3)

Prove that by using the principle of mathematical induction for all n in N : 1.3+3.5+5.7+....+(2n-1)(2n+1)= (n(4n^(2)+6n-1))/(3)