= \(\frac{9}{1x4}+\frac{9}{4x7}+\frac{9}{7x10}+.........+\frac{9}{19x22}+\frac{9}{22x25}\)
= \(\frac{1}{3}x\left(\frac{9}{1}-\frac{9}{4}\right)+\left(\frac{9}{4}-\frac{9}{7}\right)x\frac{1}{3}+........+\left(\frac{9}{22}-\frac{9}{25}\right)x\frac{1}{3}\)
= \(\frac{1}{3}\left(\frac{9}{1}-\frac{9}{4}+\frac{9}{4}-\frac{9}{7}+....+\frac{9}{22}-\frac{9}{25}\right)\)
= \(\frac{1}{3}x\left(\frac{9}{1}-\frac{9}{25}\right)\)
= \(\frac{1}{3}x\frac{216}{25}\)
= \(\frac{72}{25}\)
nhớ ********** nha bn thân
\(\frac{9}{4}+\frac{9}{28}+\frac{9}{70}+\frac{9}{130}+...+\frac{9}{418}+\frac{9}{550}\)
\(=3\left(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{19.22}+\frac{3}{22.25}\right)\)
\(=3\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{22}-\frac{1}{25}\right)\)
\(=3\left(1-\frac{1}{25}\right)\)
\(=3.\frac{24}{25}=\frac{72}{25}\)
