Cho biểu thức sau: \(P=\frac{1}{5}+\frac{2}{5^2}+\frac{3}{5^3}+\frac{4}{5^4}+.....+\frac{2015}{5^{2015}}+\frac{2016}{5^{2016}}\)

Chứng minh 1/4 < P< 1/3 

chứng minh \(A=\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+...+\frac{4031}{2015^2.2016^2}< 1\)

Cho \(A=\frac{1}{5}+\frac{2}{5^2}+\frac{3}{5^3}+\frac{4}{5^4}+...+\frac{2015}{5^{2015}}\)

CMR a) A<1

        b) A<\(\frac{1}{16}\)

CHỨNG MINH RẰNG

\(\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+......+\frac{4031}{2015^2.2016^2}< 1\)

A =\(\frac{2015+\frac{2014}{2}+\frac{2013}{3}+\frac{2012}{4}+\frac{2011}{5}+.....+\frac{1}{2015}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+......+\frac{1}{2016}}=\)

tìm A

Cho N=\(\frac{2}{1}.\frac{4}{3}.\frac{6}{5}...\frac{2016}{2015}\). Chứng minh rằng N<52

Cho \(B=\frac{1}{5^2}+\frac{2}{5^3}+\frac{3}{5^4}+...+\frac{2014}{5^{2015}}\)

Chứng tỏ rằng : B < \(\frac{1}{16}\)

Chứng minh \(\frac{\sqrt{2}-\sqrt{1}}{3}+\frac{\sqrt{3}-\sqrt{2}}{5}+\frac{\sqrt{4}-\sqrt{3}}{7}+...+\frac{\sqrt{2015}-\sqrt{2014}}{4029}