MathDB
B.Math - integer part

Source:

June 20, 2012
calculusintegration

Problem Statement

For any k∈Z+k\in\mathbb{Z}^+ , prove that:-
2(k+1−k)<1k<2(k−k−1)2(\sqrt{k+1}-\sqrt{k})<\frac{1}{\sqrt{k}}<2(\sqrt{k}-\sqrt{k-1})
Also compute integral part of 12+13+...+110000\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{10000}}.
Back to ProblemsView on AoPS