thế này à:
\(\frac{91-\frac{1}{11}-\frac{2}{12}-\frac{3}{13}-...-\frac{91}{101}}{\frac{1}{55}+\frac{1}{60}+....+\frac{1}{505}}\)
\(\frac{91-\frac{1}{11}-\frac{2}{12}-\frac{3}{13}-...-\frac{91}{101}}{\frac{1}{55}+\frac{1}{60}+\frac{1}{65}+...+\frac{1}{505}}\)
Xét tử:
\(91-\frac{1}{11}-\frac{2}{12}-\frac{3}{13}-...-\frac{91}{101}\)
= \(\left(1+1+1+...+1\right)-\left(\frac{1}{11}+\frac{2}{12}+\frac{3}{13}+...+\frac{91}{101}\right)\)
= \(\left(1-\frac{1}{11}\right)+\left(1-\frac{2}{12}\right)+....+\left(1-\frac{91}{101}\right)\)
= \(\frac{10}{11}+\frac{10}{12}+...+\frac{10}{101}\)
= \(10.\left(\frac{1}{11}+\frac{1}{12}+...+\frac{1}{101}\right)\)
= \(10.5.\left(\frac{1}{55}+\frac{1}{60}+...+\frac{1}{505}\right)\)
= \(50.\left(\frac{1}{55}+\frac{1}{60}+...+\frac{1}{505}\right)\)
Thay vào ta được phân số:
\(\frac{50.\left(\frac{1}{55}+\frac{1}{60}+...+\frac{1}{505}\right)}{\frac{1}{55}+\frac{1}{60}+...+\frac{1}{505}}\)
= 50
