Separate odd-index and even-index denominator terms

Given $A_n=\sum_{r=1}^n1/[r(r+2)]=3/4-1/[2(n+1)]-1/[2(n+2)]$:

(i) Deduce $A_n<3/4$ for all positive integers $n$.1 mark

(ii) Given also $\sum_{r=1}^n1/[r(r+1)]=1-1/(n+1)$, find $\sum_{r=1}^n1/[2r(2r+2)]$.2 marks

(iii) Use these results to find $\sum_{r=1}^n1/(4r^2-1)$ in terms of $n$.4 marks