For x∈R, let [x] denotes the greatest integer ≤ x, then the value of −13+−13−1100+−13−2100+,…,+−13−99100 is

For 0≤r≤66,0≤r100<23⇒ −23<−r100≤0⇒ −13−23<−13−r100≤−13∴ −13−r100=−1 for 0≤r≤66Also, for 67≤r≤100,67100≤r100≤1⇒ −1≤−r100≤−67100⇒ −13−1≤−13−r100≤−13−67100∴ −13−r100=−2 for 67≤r≤100Hence, ∑r=0100 −13−r100=67(−1)+2(−34)=−135