\(A< \frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2007.2009}=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2007}-\frac{1}{2009}=\frac{1}{3}-\frac{1}{2009}=\frac{2006}{6027}< \frac{2006}{4016}=\frac{1003}{2008}\)Vây:.......
Các câu hỏi tương tự
Cho A = \(\frac{2}{3^2}+\frac{2}{5^2}+\frac{2}{7^2}+...+\frac{2}{2007^2}\)Chứng minh rằng : A< 1003/2008
Chứng minh \(A=\frac{2}{3^2}+\frac{2}{5^2}+\frac{2}{7^2}+...+\frac{2}{2007^2}
Cho \(B=\frac{2}{3^2}+\frac{2}{5^2}+\frac{2}{7^2}+.....+\frac{2}{2007^2}\). Chứng minh: A<\(\frac{1003}{2008}\)
CHO A =\(\frac{2}{3^2}+\frac{2}{5^2}+\frac{2}{7^2}+...+\frac{2}{2007^2}\)
CHUNG MINH A <\(\frac{1003}{2008}\)
Cho A = \(\frac{2}{3^2}\)+ \(\frac{2}{5^2}\) + \(\frac{2}{7^2}\)+ ... + \(\frac{2}{2007^2}\) Chứng minh: A < \(\frac{1003}{2008}\)
Chứng minh rằng :
\(\frac{2}{3^2}\)+\(\frac{2}{5^2}\)+...+\(\frac{2}{2007^2}\)< \(\frac{1003}{2008}\)
\(CM:A=\frac{2}{3^2}+\frac{2}{5^2}+...+\frac{2}{2007^2}< \frac{1003}{2008}\)
\(B=\frac{2}{3^2}+\frac{2}{5^2}+\frac{2}{7^2}+...+\frac{2}{2015^2}\)
Chứng minh B<\(\frac{1003}{2008}\)
a, Tính nhanh :
\(\frac{2009\times(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2007}+\frac{1}{2008})}{2008-\left(\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+...+\frac{2006}{2007}+\frac{2007}{2008}\right)}\)
b, Cho \(\text{Q}=2+2^2+2^3+...+2^{10}\). Chứng tỏ rằng \(Q⋮3\).