Show that $\Sigma_{j=1}^{n} 1/j(j+1) = \dfrac{n}{n+1}$

Question

Show that $\Sigma_{j=1}^{n} \dfrac{1}{j(j+1)} = \dfrac{n}{n+1}$

I am having trouble trying to show this since this series doesnt seem to represent any arithmetic or geometric form of common difference.

Hint: $1=1+j-j$. – Jonatan B. Bastos Oct 05 '17 at 23:44 — Jonatan B. Bastos, Oct 05 '17 at 23:44
So far we have no use of partial fractions in the class. – Killimanjaro Oct 05 '17 at 23:44 — Killimanjaro, Oct 05 '17 at 23:44

score 0 · Answer 1 · answered Oct 05 '17 at 23:47

0

a very classic hint: $\dfrac{1}{j(j+1)} = \dfrac{1}{j} - \dfrac{1}{j+1}$. Are you aware of this one ?

answered Oct 05 '17 at 23:47

DeepSea

1 Answers1