Question

tính nhanh 4/2x4 + 4/4x6 + 4/6x8 + .... + 4/2008x 2010

Answer 1

Đặt:A =  \(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+.....+\frac{4}{2008.2010}\)

=> A = 2.(\(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+.....+\frac{2}{2008.2010}\)

=> A = 2.(\(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+.....+\frac{1}{2008}-\frac{1}{2010}\)

=> A = 2.(\(\frac{1}{2}-\frac{1}{2010}\))

=> A = 2.\(\frac{502}{1005}\)

=> A = \(\frac{1004}{1005}\)

Answer 2

đặt A= \(\frac{4}{2.4}+\frac{4}{4.6}+...+\frac{4}{2008.2010}\) 

=> 1/2.A=\(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{2008.2010}\) 

= \(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2008}-\frac{1}{2010}\)

=\(\frac{1}{2}-\frac{1}{2010}\)

=\(\frac{502}{1005}\)

Vậy biểu thức cần tìm có giá trị là \(\frac{502}{1005}\)

Answer 3

nhầm nha

=> A= \(\frac{502}{1005}:\frac{1}{2}\)=\(\frac{1004}{1005}\)