#)Giải :
\(\frac{91}{1.4}+\frac{91}{4.7}+\frac{91}{7.11}+...+\frac{91}{88.91}\)
\(=\frac{91}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.11}+...+\frac{3}{88.91}\right)\)
\(=\frac{91}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{88}-\frac{1}{91}\right)\)
\(=\frac{91}{3}\left(1-\frac{1}{91}\right)\)
\(=\frac{91}{3}.\frac{90}{91}=30\left(đpcm\right)\)
#~Will~be~Pens~#
\(\frac{91}{1\cdot4}+\frac{91}{4\cdot7}+...+\frac{91}{88\cdot91}=\frac{1}{3}\left(91-\frac{91}{4}+\frac{91}{4}-\frac{91}{7}+...-\frac{91}{91}\right)\)
\(=\frac{1}{3}\left(91-1\right)=\frac{1}{3}\cdot90=30\)
Ta có :
\(\frac{91}{1.4}+\frac{91}{4.7}+\frac{91}{7.10}+...+\frac{91}{88.91}\)
\(=\frac{91}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{88.91}\right)\)
\(=\frac{91}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{88}-\frac{1}{91}\right)\)
\(=\frac{91}{3}.\left[1+\left(\frac{1}{4}-\frac{1}{4}\right)+\left(\frac{1}{7}-\frac{1}{7}\right)+...+\left(\frac{1}{88}-\frac{1}{88}\right)-\frac{1}{91}\right]\)
\(=\frac{91}{3}.\left[1-\frac{1}{91}\right]\)
\(=\frac{91}{3}.\frac{90}{91}\)
\(=\frac{8190}{273}=30\)
Vì \(30=30\)nên \(\frac{91}{1.4}+\frac{91}{4.7}+\frac{91}{7.10}+...+\frac{91}{88.91}=30\)
~ Hok tốt ~