Question

[Hồng Phong Đoàn]

Tính tỉ số , biết:

Answer 1

[Nguyễn Thị Thương Hoài]

A = \(\dfrac{1}{2}\) + \(\dfrac{1}{3}\) + \(\dfrac{1}{4}\) +...+ \(\dfrac{1}{2007}\) + \(\dfrac{1}{2008}\) + \(\dfrac{1}{2009}\)

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

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

B = \(\dfrac{2+2007}{2}\)   +  \(\dfrac{3+2006}{3}\) +... + \(\dfrac{2007+2}{2007}\) + \(\dfrac{2008+1}{2008}\) + \(\dfrac{2009}{2009}\)

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

B = 2009.( \(\dfrac{1}{2}\) + \(\dfrac{1}{3}\) + ....+ \(\dfrac{1}{2007}\) + \(\dfrac{1}{2008}\) + \(\dfrac{1}{2009}\))

Tỉ số của \(\dfrac{A}{B}\) 

\(\dfrac{A}{B}\)=  \(\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2007}+\dfrac{1}{2008}+\dfrac{1}{2009}}{2009.\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2007}+\dfrac{1}{2008}+\dfrac{1}{2009}\right)}\)

\(\dfrac{A}{B}\) = \(\dfrac{1}{2009}\)