`(1)/(1.4)+(1)/(4.7)+(1)/(7.10)+...+(1)/((3n-2)(3n+1))=(n)/(3n+1)`

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))

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)

underset(n to oo)lim {(1)/(1.4)+(1)/(4.7)+(1)/(7.10)+....+(1)/((3n-2)(3n+1))}=

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

Prove the following by the principle of mathematical induction: (1)/(3.7)+(1)/(7.11)+(1)/(11.15)++(1)/((4n-1)(4n+3))=(n)/(3(4n+3))

For all ninNN , prove by principle of mathematical induction that, (1)/(1*4)+(1)/(4*7)+(1)/(7*10)+ . . . to terms =(n)/(3n+1) .

lim_(n rarr oo)((1)/(1.4)+(1)/(4.7)++(1)/((3n-2)(3n+1))))

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

Show that (C_(0))/(1) - (C_(1))/(4) + (C_(2))/(7) - … + (-1)^(n) (C_(n))/(3n +1) = (3^(n) * n!)/(1*4*7…(3n+1)) , where C_(r) stands for ""^(n)C_(r) .