T
tranpro123


câu 1. với k luôn dương cm
[TEX]\frac{1}{(k+1)\sqrt{k}}\prec 2\left(\frac{1}{\sqrt{k}}-\frac{1}{\sqrt{k+1}} \right)[/TEX]
câu 2. dễ thui Rút gọn
[TEX]\sqrt{1+\frac{1}{{2}^{2}}+\frac{1}{{3}^{2}}}+\sqrt{1+\frac{1}{{3}^{2}}+\frac{1}{{4}^{2}}}+...+\sqrt{1+\frac{1}{{2009}^{2}}+\frac{1}{{2010}^{2}}[/TEX]
[TEX]\frac{1}{(k+1)\sqrt{k}}\prec 2\left(\frac{1}{\sqrt{k}}-\frac{1}{\sqrt{k+1}} \right)[/TEX]
câu 2. dễ thui Rút gọn
[TEX]\sqrt{1+\frac{1}{{2}^{2}}+\frac{1}{{3}^{2}}}+\sqrt{1+\frac{1}{{3}^{2}}+\frac{1}{{4}^{2}}}+...+\sqrt{1+\frac{1}{{2009}^{2}}+\frac{1}{{2010}^{2}}[/TEX]