MathDB

floor + sum

Source: 1996 Korea National Olympiad #3

March 22, 2018

floor functionalgebra

Problem Statement

Let

a=\lfloor \sqrt{n} \rfloor

for given positive integer

n.

Express the summation

\sum_{k=1}^{n}\lfloor \sqrt{k} \rfloor

in terms of

n

and

a.