Using mathematical induction prove that `1^3+2^3+3^3+.....+n^3=[(n(n+1))/2]^2`

Using mathematical induction prove that 1^2+3^2+5^2+.....+(2n-1)^2=(n(2n-1)(2n+1))/3 for all n in N

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

Using mathematical induction prove that 1cdot2+2cdot2^2+......+ncdot2^n=(n-1)2^(n+1)+2 for all n in N

Using mathematical induction prove that P(n) = 1+3+5+........... +2n-1=n^(2)

Using mathematical induction prove that 1/(1.2.3)+1/(2.3.4)+......+1/(n(n+1)(n+2))=(n(n+3))/(4(n+1)(n+2)) for all n in N .

Using mathematical induction prove 1cdot3+2cdot3^2+3cdot3^3+.....+ncdot3^n=((2n-1)3^(n+1)+3)/4 for all n in N

Using mathematical induction prove that (2n+7) lt (n+3)^2 for all n in N

Using mathematical induction prove that (1+3/1)(1+5/4)(1+7/9)......(1+(2n+1)/n^2)=(n+1)^2 for all n in N

Using mathematical induction prove that 1cdot3+3cdot5+5cdot7+.....+(2n-1)(2n+1)=(n(4n^2+6n-1))/3 true for all n in N

Using mathematical induction prove that (1+1/1)(1+1/2)(1+1/3)......(1+1/n)=n+1 for all n in N