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 1cdot2+2cdot2^2+......+ncdot2^n=(n-1)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 1^3+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

Using mathematical induction prove that (2n+7) lt (n+3)^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/(3.5)+1/(5.7)+1/(7.9)+.......+1/((2n+1)(2n+3))=n/(3(2n+3) for all n in N

Using mathematical induction prove that 1/(1.4)+1/(4.7)+1/(7.10)+.......+1/((3n-2)(3n+1))=n/(3n+1) 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 mathimatical induction prove that 1/(2.5)+1/(5.8)+1/(8.11)+......+1/((3n-1)(3n+2))=n/(6n+4) for all n in N .