\(\frac{2}{2.5}+\frac{2}{5.8}+\frac{2}{8.11}+...+\frac{2}{14.17}=2.\left(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{14.17}\right)\)
\(=\frac{2}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{14}-\frac{1}{17}\right)\)
\(=\frac{2}{3}.\left(\frac{1}{2}-\frac{1}{17}\right)=\frac{2}{3}.\frac{15}{34}=\frac{5}{17}\)
\(\frac{2}{2.5}+\frac{2}{5.8}+\frac{2}{8.11}+...+\frac{2}{14.17}\)
\(=\frac{2}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{14.17}\right)\)
\(=\frac{2}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{14}-\frac{1}{17}\right)\)
\(=\frac{2}{3}.\left(\frac{1}{2}-\frac{1}{17}\right)\)
\(=\frac{2}{3}.\left(\frac{17}{34}-\frac{2}{34}\right)\)
\(=\frac{2}{3}.\frac{15}{34}=\frac{5}{17}\)
\(\frac{2}{2.5}+\frac{2}{5.8}+\frac{2}{8.11}+...+\frac{2}{14.17}\)
\(=\frac{2}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{14.17}\right)\)
\(=\frac{2}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{14}-\frac{1}{17}\right)\)
\(=\frac{2}{3}.\left(\frac{1}{2}-\frac{1}{17}\right)\)
\(=\frac{2}{3}.\frac{16}{34}=\frac{16}{51}\)
Đặt biểu thức trên bằng A
A=\(\frac{2}{2.5}\)+\(\frac{2}{5.8}\)+\(\frac{2}{8.11}\)+...+\(\frac{2}{14.17}\)
\(\frac{3}{2}\)A=\(\frac{3}{2.5}\)+\(\frac{3}{5.8}\)+\(\frac{3}{8.11}\)+...+\(\frac{3}{14.17}\)
\(\frac{3}{2}\)A=\(\frac{1}{2}\)-\(\frac{1}{5}\)+\(\frac{1}{5}\)-\(\frac{1}{8}\)+\(\frac{1}{8}\)-\(\frac{1}{11}\)+...+\(\frac{1}{14}\)-\(\frac{1}{17}\)
\(\frac{3}{2}\)A=\(\frac{1}{2}\)-\(\frac{1}{17}\)=\(\frac{15}{34}\)
=>A=\(\frac{15}{34}\)x\(\frac{2}{3}\)=\(\frac{5}{17}\)
k đúng nha ban
đặt A =2 / 2.5 + 2 / 5.8 + 2/ 8.11 + ............. + 2/ 14.17
A=2/3.3/2.5 + 2/3.3/5.8 + 2/3.3/8.11 + ........+ 2/3.3/14.17
A=2/3.(3/2.5 + 3/5.8 + 3/8.11 + ........ + 3/14.17)
A=2/3.( 1/2-1/5 + 1/5-1/8 + 1/8-1/11 + ....... + 1/14-1/17 )
A=2/3.(1/2-1/17 )
A=2/3.15/34
A= 5/17