[" Principle of MATHEMATICAL INDUCTION "],[" 8.Frove the follocoing by using PMI tor all "],[" i) "1+4+7+-cdots+(3n-2)=(1)/(2)n(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 in N : 1+4+7++(3n-2)=1/2n(3n-1)

By the Principle of Mathematical Induction, prove the following for all n in N : 1+4+7+.....+ (3n-2)= (n(3n-1))/2 .

Prove the following by using the principle of mathematical induction for all n in Nvdots1+2+3+...+n<(1)/(8)(2n+1)^(2)

By the Principle of Mathematical Induction, prove the following for all n in N : 2^(3n)-1 is divisible by 7 .

By using the Principle of Mathematical Induction, prove the following for all n in N : x+4x+7x+......+(3n-2)x=1/2n (3n-1) x .

By the Principle of Mathematical Induction, prove the following for all n in N : 1/1.3+1/3.5+1/5.7+......+ 1/((2n -1)(2n +1))= n/(2n +1) .

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

By using mathematical induction prove that 1+4+7+...+(3n-2)=(n(3n-1))/2

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