=1/2-1/4+1/4-1/6+1/61/8+1/81/10+1/10-1/12
=1/2-1/12
5/12
tk nha
Đặt : \(A=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+\frac{1}{10.12}\)
\(\Rightarrow2A=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+\frac{2}{10.12}\)
\(\Rightarrow2A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+......+\frac{1}{10}-\frac{1}{12}\)
\(\Rightarrow2A-A=\frac{1}{2}-\frac{1}{12}\)
\(\Rightarrow A=\frac{5}{12}\)
bài duoi giải sai nha
Dặt biểu thức trên là A
ta có\(2A=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+\frac{2}{10.12}\)
\(2A=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{10}-\frac{1}{12}\)
\(2A=1-\frac{1}{12}=\frac{11}{12}\)
\(A=\frac{11}{12}\)/ 2=\(\frac{11}{24}\)
\(\frac{1}{2x4}+\frac{1}{4x6}+\frac{1}{6x8}+\frac{1}{8x10}+\frac{1}{10x12}=A\)
\(\frac{2}{2x4}+\frac{2}{4x6}+\frac{2}{6x8}+\frac{2}{8x10}+\frac{2}{10x12}=Ax2\)
\(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+\frac{1}{10}-\frac{1}{12}=Ax2\)
\(\frac{1}{2}-\frac{1}{12}=\frac{5}{12}x2=\frac{5}{6}\)
bỏ dòng cuối sửa lại:
\(\frac{1}{2}-\frac{1}{12}=\frac{5}{12}:2=\frac{5}{24}\)
1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10+1/10-1/12
=1/2-1/12=5/12*2=5/6
