Question

What is the closed form of:\[\sum_{n=1}^{k} \frac{1}{n(n+1)}\]

Answer 1

looks sooo familiar lol

Answer 2

well no recursive cancellation like before XD

Answer 3

1-{1/(n+1)}
correct?

Answer 4

closed for so that has to be in variable k

Answer 5

it not infinite series

Answer 6

1-{1/(k+1)}

Answer 7

doncatch can u explain how u got that..

Answer 8

doncatch is right

Answer 9

it is easy .....
1/n.(n+1) = 1/n - 1/(n+1)
so sum = (1/2-1/3)+(1/3-1/4)+(1/4-1/5)+....+(1/k-1/k+1)
so sum = 1-1/(1+K)
Di u unerstan?