Answer to Question #36924 in Combinatorics | Number Theory for Quamrul

Question

Consider the sequence 1, 2, 3, … k. You have to put a ‘+’ or ‘–’ sign between these
numbers so that the sum becomes zero (e.g. if k is 4, you can do it like 1 – 2 – 3 + 4 = 0).
For how many values of k between 2001 and 2100 (both inclusive) this can be done?