Challenge question - Use integral calculus.

Jun 2014
945
191
Earth
.

This was posted under "Arithmetic."

Use integral calculus.


What is $\lfloor x \rfloor$ if

$$x=\frac1{\sqrt2} \ + \ \sqrt1 \ + \ \frac1{\sqrt4} \ + \ \sqrt3 \ + \ \ldots \ + \ \frac1{\sqrt{2016}} \ + \ \sqrt{2015} \ ?$$