CMR:
\(\frac{1}{2^3}+\frac{1}{3^3}+\frac{1}{4^3}+...+\frac{1}{2016^3}< \frac{1}{4}\)
Những câu hỏi liên quan
CMR:
\(\frac{1}{2^3}+\frac{1}{3^3}+\frac{1}{4^3}+...+\frac{1}{2016^3}< \frac{1}{4}\)
CMR:
\(\frac{1}{2^3}+\frac{1}{3^3}+\frac{1}{4^3}+...+\frac{1}{2016^3}< \frac{1}{4}\)
CMR:
\(\frac{1}{2^3}+\frac{1}{3^3}+\frac{1}{4^3}+...+\frac{1}{2016^3}< \frac{1}{4}\)
CMR:
\(\frac{1}{2^3}+\frac{1}{3^3}+\frac{1}{4^3}+...+\frac{1}{2016^3}< \frac{1}{4}\)
\(\frac{1}{2^3}+\frac{1}{3^3}+\frac{1}{4^3}+...+\frac{1}{2016^3}\)
=\(\frac{1}{2x2x2}+\frac{1}{3x3x3}+\frac{1}{4x4x4}+...+\frac{1}{2016x2016x2016}\)
Ta có:\(\frac{1}{2x2x2}< \frac{1}{1x2x3}\)
........................................................(Tương tự)
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CMR:
\(\frac{1}{2^3}+\frac{1}{3^3}+\frac{1}{4^3}+...+\frac{1}{2016^3}< \frac{1}{4}\)
Cho \(A=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2017};B=\frac{2016}{1}+\frac{2015}{2}+\frac{2014}{3}+...+\frac{1}{2016}\).CMR B/A là số nguyên
Ta có :
\(B=\frac{2016}{1}+\frac{2015}{2}+\frac{2014}{3}+...+\frac{1}{2016}\)
\(B=\left(\frac{2015}{2}+1\right)+\left(\frac{2014}{3}+1\right)+...+\left(\frac{1}{2016}+1\right)+1\)
\(B=\frac{2017}{2}+\frac{2017}{3}+...+\frac{2017}{2016}+\frac{2017}{2017}\)
\(B=2017.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2016}+\frac{1}{2017}\right)\)
\(\Rightarrow\frac{B}{A}=\frac{2017.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2016}+\frac{1}{2017}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2017}}=2017\)
Vậy \(\frac{B}{A}\)là số nguyên
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Cho \(E=\frac{1}{3}+\frac{2}{3^2}-\frac{3}{3^3}+\frac{4}{3^4}-...+\frac{2016}{3^{2016}}-\frac{2017}{3^{2017}}\)
CMR : \(E< \frac{3}{16}\)
Rút gọn:
\(\frac{2016-\frac{1}{2}-\frac{1}{3}-\frac{1}{4}-...-\frac{1}{2017}}{\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+...+\frac{2015}{2016}}\)
cmr\(\frac{1}{2\sqrt{1}}+\frac{1}{3\sqrt{2}}+\frac{1}{4\sqrt{3}}+...+\frac{1}{2016\sqrt{2015}}
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