`1/3.7+1/7.11+1/11.15+.......+1/((4n-1)(4n+3))=n/(3(4n+3))`

Prove the following by using the principle of mathematical induction for all n in Nvdots(1)/(1.4)+(1)/(4.7)+(1)/(7.10)+...+(1)/((3n-1)(3n+1))=(n)/((3n+1))

1.3+3.5+5.7+......+(2n-1)(2n+1)=(n(4n^(2)+6n-1))/(3)

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

(1)/(1.2)+(1)/(2.3)+(1)/(3.4)+.......+(1)/(n(n+1))=(n)/(n+1),n in N is true for

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 the principle of mathematical induction: (1)/(1.4)+(1)/(4.7)+(1)/(7.10)++(1)/((3n-1)(3n+2))=(n)/(3n+1)

(1^(4))/(1.3)+(2^(4))/(3.5)+(3^(4))/(5.7)+......+(n^(4)) /((2n-1)(2n+1))=(n(4n^(2)+6n+5))/(48)+(n)/(16(2n+1))

1.2+2.3+3.4+.........+n(n+1)=(1)/(3)n(n+1)(n+3)

Using the principle of mathematical induction, prove each of the following for all n in N 1/(1*4)+1/(4*7) + 1/(7*10) +…+1/((3n-2)(3n+1)) = n/((3n+1)) .