Good day, I would like to solve this problem using the theorem of the comparison, but I do not understand how to proceed, can anyone help me?
How do I prove that $(v_n)$, defined by $v_n:= \frac{1}{\sqrt{n^2+1}}+\frac{1}{\sqrt{n^2+2}}+\cdots +\frac{1}{\sqrt{n^2+n}},$ is convergent?