गणितीय आगमन की सिद्धांत का प्रयोग करंट हुए सिद्ध कीजिये की
`(1)/(1.4)+(1)/(4.7)+(1)/(7.10)+..+(1)/((3n-2)(3n+1))=((n)/(3n+1))`

1/1.4+1/4.7+1/7.10+...+1/((3n-2)(3n+1))=n/((3n+1)) forall n in N.

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

lim_(n rarr oo)((1)/(1.4)+(1)/(4.7)++(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 that by using the principle of mathematical induction for all n in N : (1)/(1.4)+ (1)/(4.7)+(1)/(7.10)+...+ (1)/((3n-2)(3n+1))= (n)/(3n+1)

Prove that by using the principle of mathematical induction for all n in N : (1)/(1.4)+ (1)/(4.7)+(1)/(7.10)+...+ (1)/((3n-2)(3n+1))= (n)/(3n+1)

Prove that by using the principle of mathematical induction for all n in N : (1)/(1.4)+ (1)/(4.7)+(1)/(7.10)+...+ (1)/((3n-2)(3n+1))= (n)/(3n+1)

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

By using the principle of mathematical induction , prove the follwing : (1)/(1.4) + (1)/(4.7) + (1)/(7.10) + ………..+ (1)/((3n - 2)(3n+1)) = (n)/(3n + 1) , n in N

Prove the following by using the principle of mathematical induction for all n in N (1)/(1.4)+(1)/(4.7)+ (1)/(7.10)+…….+(1)/((3n -2)(3n+1)) = (n)/(3n+1)