Question

A=4\2×4+4\4×6+4\6×8+....+4\2010×2012

Answer 1

\(A=\frac{4}{2\cdot4}+\frac{4}{4\cdot6}+\frac{4}{6\cdot8}+...+\frac{4}{2010\cdot2012}\)

\(\Rightarrow\frac{2}{4}A=\frac{2}{4}\left(\frac{4}{2\cdot4}+\frac{4}{4\cdot6}+\frac{4}{6\cdot8}+.....+\frac{4}{2010\cdot2012}\right)\)

\(\Rightarrow\frac{2}{4}A=\frac{2}{2\cdot4}+\frac{2}{4\cdot6}+\frac{2}{6\cdot8}+...+\frac{2}{2010\cdot2012}\)

\(\Rightarrow\frac{2}{4}A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+....+\frac{1}{2010}-\frac{1}{2012}\)

\(\Rightarrow\frac{2}{4}A=\frac{1}{2}-\frac{1}{2012}\Rightarrow\frac{2}{4}A=\frac{1005}{2012}\)

\(\Rightarrow A=\frac{1005}{2012}:\frac{2}{4}\Rightarrow A=\frac{1005}{1006}\)

Answer 2

May cai gach la phan nhe

Answer 3

\(A=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2010.2012}\)

\(A=2\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2010.2012}\right)\)

\(A=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2010}-\frac{1}{2012}\right)\)

\(A=2\left(\frac{1}{2}-\frac{1}{2012}\right)=2\left(\frac{1006}{2012}-\frac{1}{2012}\right)=2.\frac{1005}{2012}\)

\(A=\frac{2.1005}{2012}=\frac{1.1005}{1006}=\frac{1005}{1006}\)

Answer 4

Thanks nha 😂😂