Using the principle of mathematical induction prove that `1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)++1/(1+2+3++n)=(2n)/(n+1)` for all `n in N`

Using the principle of mathematical induction, prove that 1/(1*2)+1/(2*3)+1/(3*4)+…+1/(n(n+1)) = n/((n+1)) .

By using principle of mathematical induction, prove that 2+4+6+….2n=n(n+1), n in N

Using the principle of mathematical induction, prove that (1-1/2)(1-1/3)(1-1/4)...(1-1/(n+1))= 1/((n+1))" for all " n in N .

Using principle of mathematical induction, prove the following 1+3+5+...+(2n-1)=n^(2)

Using the principle of mathematical induction, prove that (2^(3n)-1) is divisible by 7 for all n in N

Using the principle of mathematical induction prove that (1+x)^(n)>=(1+nx) for all n in N, where x>-1

Using the principle of mathematical induction , prove that for n in N , (1)/(n+1) + (1)/(n+2) + (1)/(n+3) + "……." + (1)/(3n+1) gt 1 .

Using the principle of mathematical induction prove that : the 1.3+2.3^(2)+3.3^(3)++n.3^(n)=((2n-1)3^(n+1)+3)/(4) for all n in N.

Using the principle of mathematical induction prove that (1)/(1.2.3)+(1)/(2.3.4)+(1)/(3.4.5)+...+(1)/(n(n+1)(n+2))=(n(n+3))/(4(n+1)(n+2) for all n in N

Prove by using the principle of mathemtical induction: 1+2+3+…+n =(n(n+1))/2