TargetIIT

The set of integers is divided into n infinite APs.

If the common differences of the APs are denoted by d[ss]i[/ss], find [im]http://codecogs.izyba.com/gif.latex?%5Csum_%7Bi%3D1%7D%5En%20%5Cfrac%7B1%7D%7Bd_i%7D[/im]

sir we can state that the common difference must be same for all ap's
so hence n will also be d
so
S=n/d =1

that's right, but I am not gonna break into song and dance until I see some watertight reasoning

sir
the common difference must be same for all ap's
if they are not same they there will be common terms

prove it, sweetheart.