Question

[Uan Le]

Tính nhanh 

C= 4 phần 2 nhân 4 + 4 phan   4 nhân 6+ 4 phần 6 nhân 8+........+4 phần 2008 nhân 2010

Answer 1

[I don't need you]

\(C=\frac{4}{2\times4}+\frac{4}{4\times6}+\frac{4}{6\times8}+...+\frac{4}{2008\times2010}\)

\(C=2\times\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)

\(C=2\times\left(\frac{1}{2}-\frac{1}{2010}\right)\)

\(C=2\times\frac{502}{1005}\)

\(C=\frac{1004}{1005}\)

Answer 2

[Đỗ Ngọc Hải]

\(C=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)
\(C=2\left(\frac{4-2}{2.4}+\frac{6-4}{4.6}+\frac{8-6}{6.8}+...+\frac{2010-2008}{2008.2010}\right)\)
\(C=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)
\(C=2\left(\frac{1}{2}-\frac{1}{2010}\right)\)
\(C=\frac{1004}{1005}\)