Prove by the principle of mathematical induction that for all `n N :\ ` `1/(1. 3)+1/(35)+1/(57)++1/((2n-1)(2n+1))=n/(2n+1)`

Prove by the principle of mathematical induction that for all nN:(1)/(1.3)+(1)/(35)+(1)/(57)++(1)/((2n-1)(2n+1))=(n)/(2n+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^(2)+2^(2)+3^(2)+...+n^(2)=(1)/(6)n(n+1)(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)

Using the principle of mathmatical induction, prove each of 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 Nvdots(1)/(3.5)+(1)/(5.7)+(1)/(7.9)+...+(1)/((2n+1)(2n+3))=(n)/(3(2n+3))

Prove the following by using the principle of mathematical induction for all n in Nvdots(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))

Prove the following by using the principle of mathematical induction for all n in Nvdots(1)/(2.5)+(1)/(5.8)+(1)/(8.11)+...+(1)/((3n-1)(3n+2))=(n)/((6n+4))=(n)/((6n+4))

Prove the following by the principle of mathematical induction: (1)/(3.5)+(1)/(5.7)+(1)/(7.9)+(1)/((2n+1)(2n+3))=(n)/(3(2n+3))

Prove by the principle of mathematical induction that n(n+1)(2n+1) is divisible by 6 for all n in N