\(=\left(1-\dfrac{1}{99}-1-\dfrac{1}{97}+\dfrac{1}{97}-\dfrac{1}{98}\right)\cdot\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}\right)\)
\(=\left(-\dfrac{1}{99}-\dfrac{1}{98}\right)\cdot\dfrac{3}{10}=\dfrac{-197\cdot3}{9702\cdot10}=\dfrac{-197}{32340}\)
BT2: Tính nhanh
11) \(\left(\dfrac{99}{98}-\dfrac{98}{97}+\dfrac{1}{98.97}\right).\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}\right)\)
12) \(\dfrac{7}{17}+\dfrac{10}{17}\left(\dfrac{-3}{5}+\dfrac{1}{2}\right)^2\)
BT1: Tính nhanh:
2) ( \(\dfrac{98}{99}+\dfrac{89}{100}+\dfrac{100}{101}\)) . ( \(\dfrac{1}{12}-\dfrac{1}{3}+\dfrac{1}{4}\))
Tính \(H=\dfrac{\dfrac{1}{99}+\dfrac{2}{98}+\dfrac{3}{97}+...........+\dfrac{99}{1}}{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+.............+\dfrac{1}{100}}:\dfrac{92-\dfrac{1}{9}-\dfrac{1}{10}-..............\dfrac{92}{100}}{\dfrac{1}{45}+\dfrac{1}{50}+\dfrac{1}{55}+........+\dfrac{1}{500}}\)
Help me!!!
\(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+......+\dfrac{1}{100.101}\)
\(\dfrac{x+1}{99}+\dfrac{x+2}{98}+\dfrac{x+3}{97}+\dfrac{x+4}{96}=-4\)
Cho \(N=\dfrac{1.4}{2.3}+\dfrac{3.6}{3.4}+..............+\dfrac{98.101}{99.100}\) Chứng minh \(97< N< 98\)
Help me!!!!!!!!!!!!!!
BT2: Tìm x\(\in\) N*, biết
2) \(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+....+\dfrac{1}{x.\left(x+1\right)}=\dfrac{299}{600}\)
BT2: Tính nhanh
9) \(\dfrac{98}{99}+\dfrac{89}{100}+\dfrac{100}{101}.\left(\dfrac{1}{12}-\dfrac{1}{3}+\dfrac{1}{4}\right)\)
10) \(\left(\dfrac{78}{79}+\dfrac{79}{80}+\dfrac{80}{81}\right).\left(\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{3}{10}-\dfrac{2}{3}\right)\)
Giúp mk nha!
\(C=\left(\dfrac{4}{1\cdot3}\right)+\left(\dfrac{4}{3\cdot5}\right)+...+\left(\dfrac{4}{97\cdot99}\right)-\dfrac{5}{11\cdot12}-\dfrac{5}{12\cdot13}-...-\dfrac{5}{98\cdot99}\)
ok, giải nhanh cho mk nha
