A=1/2.3/4.5/6…1999/2000
CMR: A2<1/2001
Những câu hỏi liên quan
Cho C=1/2.3/4.5/6...199/200. Chứng minh rằng A2 < 1/201
TÌM x THUỘC N:2/2.3+2/3.4+2/4.5+....+2/x.(x+1)=1999/2001
Đặt \(S=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2.}{4.5}+...+\frac{2}{x\left(x+1\right)}=\frac{1999}{2001}\)
\(\Rightarrow\frac{S}{2}=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}=\frac{1999}{4002}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{1999}{4002}\)
\(=\frac{1}{2}-\frac{1}{x+1}=\frac{1999}{4002}\)
\(\frac{1}{x+1}=\frac{1}{2001}\)
\(\Rightarrow\)x+1=2001
x=2000
Vậy x=2000.
CMR :A=1/2.3/4.5/6.....99/100<1/10
đặt \(B=\frac{2}{3}.\frac{4}{5}.\frac{6}{7}...\frac{98}{99}.\frac{100}{100}\Leftrightarrow A
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A=1/2.3/4.5/6.....79/80
CMR: A<1/9
cho A=1/2.3/4.5/6.........2499/2500 chứng minh A<1/2500
so sanh A= 1/2.3/4.5/6...9999/10000 voi 0.01
chứng minh rằng : A=1/2.3/4.5/6.....99/100<1/100
Cho A=1/2.3/4.5/6. ... .9999/10000. So sánh A với 0,001
Cho A=1/2.3/4.5/6....2011/2012.Chứng minh: A^2<1/2013.