`(1- 1/(n+1))+(1-2/(n+1))+(1-3/(n+1))+…….+(1-n/(n+1))` का योग ज्ञात करें।

By using the principle of mathematical induction , prove the follwing : P(n) : (1)/(1.2) + (1)/(2.3) + (1)/(3.4) + …….+ (1)/(n(n+1)) = (n)/(n+1) , n in N

1/1.2 + 1/2.3 +…..+ 1/(n(n+1)) = n/(n+1)

((n+2)!+(n+1)(n-1)!)/((n+1)(n-1)!)=

lim_ (n rarr oo) ((1) / (n + 1) + (1) / (n + 2) + (1) / (n + 3) + ...... + (1) / (6n ))

lim_(n rarr oo) {1/n+1/(n+1)+1/(n+2)+…..+1/(3n)} =

For all ngt=1 , prove that , (1)/(1.2) + (1)/(2.3) + (1)/(3.4) + ……+ (1)/(n(n+1)) = (n)/(n+1)