Question

a) tính nhanh 

( 1 + \(\dfrac{1}{2}\) ) x ( 1 + \(\dfrac{1}{3}\) ) x ..... x ( 1 + \(\dfrac{1}{2005}\) )

b) tính bằng cách thuận tiện 

\(\dfrac{2}{3}\) x \(\dfrac{1}{2}\) + \(\dfrac{1}{3}\) x \(\dfrac{1}{2}\)

Answer 1

a)\(=\left(\dfrac{2}{2}+\dfrac{1}{2}\right)\times\left(\dfrac{3}{3}+\dfrac{1}{3}\right)\times...\times\left(\dfrac{2005}{2005}+\dfrac{1}{2005}\right)\)

\(=\dfrac{3}{2}\times\dfrac{4}{3}\times...\times\dfrac{2006}{2005}=\dfrac{2006}{2}=1003\)

b)\(=\left(\dfrac{2}{3}+\dfrac{1}{3}\right)\times\dfrac{1}{2}=\dfrac{3}{3}\times\dfrac{1}{2}=\dfrac{1}{2}\)

Answer 2

b)

\(\dfrac{1}{2}x\left(\dfrac{2}{3}+\dfrac{1}{3}\right)=\dfrac{1}{2}x1=\dfrac{1}{2}\)