Let us denote the square root of x rounded to the nearest integer by N(x).

Accordingly N(19) is equal to 4, since √(19) is less than 4.5, but N(23) is 5, because √(23) exceeds 4.5.

Using only p&p, and without a calculator, evaluate the value of this expression:

 1      1      1                   1
---- + ---- + ---- + ........ + -------
N(1)   N(2)   N(3)              N(2550)

*** Please feel free to use computer program/Excel solver aided methodology for purpose of verification.