### 2010 NYJC Promo Q5 [Modified]

2010 NYJC Promo Q5 [Modified] (i) Using partial fractions, show that $sumlimits_{n=1}^{N}{frac{1}{nleft( n+1 right)left( n+2 right)}=frac{1}{4}-frac{1}{2left( N+1 right)left( N+2 right)}}$. [4] (ii) Deduce the value of $sumlimits_{n=2}^{infty }{frac{1}{nleft( n+1 right)left(