Question

Tính A theo cách hợp lý nhất, rồi so sánh với B:

 A= \(\left(1-\frac{1}{10}\right)\left(1-\frac{1}{11}\right)\left(1-\frac{1}{12}\right)...\left(1-\frac{1}{2007}\right)\left(1-\frac{1}{2008}\right)\)

 B= \(\frac{1}{2000}\)

Chỉ trao like cho bạn nào trả lời đúng nhất, hay nhất và chính xác nhất!!

Answer 1

\(A=\left(1-\frac{1}{10}\right)\left(1-\frac{1}{11}\right)\left(1-\frac{1}{12}\right)...\left(1-\frac{1}{2007}\right)\left(1-\frac{1}{2008}\right)\)

     \(=\frac{9}{10}.\frac{10}{11}.\frac{11}{12}.....\frac{2006}{2007}.\frac{2007}{2008}\)

     \(=\frac{9.10.11.....2006.2007}{10.11.12.....2007.2008}\)

     \(=\frac{9}{2008}\)

\(Ta\) \(có:\)

\(A=\frac{9}{2008}\)

\(B=\frac{1}{2000}\)

\(\frac{9}{2008}=\frac{9.250}{2008.250}=\frac{2250}{502000}\)

\(\frac{1}{2000}=\frac{1.251}{2000.251}=\frac{251}{502000}\)

Vì \(\frac{2250}{502000}>\frac{251}{502000}\Rightarrow A>B\)

 

Answer 2

\(A=\left(1-\frac{1}{10}\right)\left(1-\frac{1}{11}\right)\left(1-\frac{1}{12}\right)...\left(1-\frac{1}{2007}\right)\left(1-\frac{1}{2008}\right)\)

\(A=\frac{9}{10}.\frac{10}{11}.\frac{11}{12}....\frac{2006}{2007}.\frac{2007}{2008}\)

\(A=\frac{9.10.11....2006.2007}{10.11.12...2007.2008}\)

\(A=\frac{9}{2008}\)

 

Vì \(\frac{9}{2008}