I tried to solve the following problem.
What is the integer part of $\frac{1}{\sqrt{1}} + \frac{1}{\sqrt{3}} + \cdots + \frac{1}{\sqrt{(2n+1)^2}}=\sum_{k=0}^{2(n^2+n)} \frac 1{\sqrt{2k+1}} ?$
I tried using some inequalities( by grouping 1,3,5,7 / 9,11,13,...,25/ ), but I failed.
How can I compute the integer part of this sum?