\(\sqrt{1.2015}\le\frac{2016}{2}\Rightarrow\frac{1}{\sqrt{1.2015}}\ge\frac{2}{2016}\)
=>S\(\ge\frac{2.1015}{2016}\)\(>\frac{2.2014}{2015}\)
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Cho Sk=\(\frac{1}{\sqrt{1.2015}}+\frac{1}{\sqrt{2.2014}}+\frac{1}{\sqrt{3.2013}}+....+\frac{1}{\sqrt{k.\left(2016-k\right)}}vớik\in N^{sao},k\le2015\)
c/m Sk>k/1018
a/Tính: A= \(\sqrt{1+2006^2+\frac{2006^2}{2007^2}}+\frac{2006}{2007}\)
b/Cho A=\(\sqrt{2015^2-1}-\sqrt{2014^2-1}\)và B=\(\frac{2.2014}{\sqrt{2015^2-1}+\sqrt{2014^2-1}}\)
So sánh A vs B
So sánh A và B:
\(A=\sqrt{2015^2-1}-\sqrt{2014^2-1}\)
\(B=\frac{2.2014}{\sqrt{2015^2-1}+\sqrt{2014^2-1}}\)
so sánh \(\sqrt{2015^2-1}-\sqrt{2014^2-1}\) và \(\frac{2.2014}{\sqrt{2015^2-1}+\sqrt{2014^2-1}}\)
Tính:
\(A=\frac{2.2014}{1+\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+...+2014}}\)
\(B=\frac{\sqrt{4+\sqrt{3}}+\sqrt{4-\sqrt{3}}}{\sqrt{4+\sqrt{13}}}+\sqrt{27-10\sqrt{2}}\)
Cho
S = \(\frac{1}{\sqrt{1.2014}}+\frac{1}{\sqrt{2.2013}}+......+\frac{1}{\sqrt{k.\left(2014-k+1\right)}}+.....+\frac{1}{\sqrt{2014.1}}\)
Hãy so sánh S với \(2.\frac{2014}{2015}\)
Cho M=\(\frac{\sqrt{2}-\sqrt{1}}{1+1}+\frac{\sqrt{3}-\sqrt{2}}{2+3}+\frac{\sqrt{4}-\sqrt{3}}{3+4}+...+\frac{\sqrt{2015}-\sqrt{2014}}{2014+2015}\)
Hãy so sánh M với 1/2
Cho S=\(\frac{1}{3\left(1+\sqrt{2}\right)}+\frac{1}{5\left(\sqrt{2}+\sqrt{3}\right)}+...+\frac{1}{97\left(\sqrt{48}+\sqrt{49}\right)}\)
So sánh S với \(\frac{3}{7}\)
S = \(\frac{1}{3\left(\sqrt{1}+\sqrt{2}\right)}+\frac{1}{5\left(\sqrt{2}+\sqrt{3}\right)}+...+\frac{1}{97\left(\sqrt{48}+\sqrt{49}\right)}\)
So sánh S với \(\frac{3}{7}\)