For x∈R,let x denote the greatest integer  ≤x  , then the sum of the series −13+−13−1100+−13−2100+.......+−13−99100is

We know thatx+x+1n+x+2n+........+x+n−1n=nxand −x=−x−1=−1−13−1−1.3+1100−1−13+2100+........−1−13+99100=−100−13100=−100−33=−133