### Solving a Strange Summation

First note that x = Floor(x) + {x}, where {} is the remainder. So if x= 2.74, then the floor is 2 + the remainder is .74 . f(x)= { 0 if x its a perfect square (like 1,4,9,...) { Floor (1/ {sqrt(x)}) otherwise So for the otherwise part, say x=2, you have 1/the remainder of sqrt(2), which is 1/.414 = 2.4