Question

Tính tỉ số \(\frac{A}{B}\)biết :

\(A=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2009}\)

\(B=\frac{2008}{1}+\frac{2007}{2}+\frac{2006}{3}+...+\frac{2}{2007}+\frac{1}{2008}\)

Answer 1

A:B=1:2

Answer 2

a:b=1:4

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Answer 3

Ko làm luôn cho người ta luôn đi mà chỉ ghi kết quả

Answer 4

Ta có : 

\(B=\frac{2008}{1}+\frac{2007}{2}+\frac{2006}{3}+...+\frac{2}{2007}+\frac{1}{2008}\)

\(B=\left(2008-1-...-1\right)+\left(\frac{2007}{2}+1\right)+\left(\frac{2006}{3}+1\right)+...+\left(\frac{2}{2007}+1\right)+\left(\frac{1}{2008}+1\right)\)

\(B=\frac{2009}{2009}+\frac{2009}{2}+\frac{2009}{3}+...+\frac{2009}{2007}+\frac{2009}{2008}\)

\(B=2009\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2009}\right)\)

\(\Rightarrow\)\(\frac{A}{B}=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2009}}{2009\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2009}\right)}=\frac{1}{2009}\)

Vậy \(\frac{A}{B}=\frac{1}{2009}\)

Chúc bạn học tốt ~ 

Answer 5

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Answer 6

Câu hỏi:

\(A=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2009}\)

\(B=\frac{2008}{1}+\frac{2007}{2}+\frac{2006}{3}+...+\frac{2}{2007}+\frac{1}{2008}\)

Trả lời:

\(\frac{A}{B}=\frac{1}{4}\)