Ta có : \(\frac{1}{10.9}-\frac{1}{9.8}-.....-\frac{1}{2.1}\)
\(=\frac{1}{90}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{9.8}\right)\)
\(=\frac{1}{90}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{8}-\frac{1}{9}\right)\)
\(=\frac{1}{90}-\left(1-\frac{1}{9}\right)\)
\(=\frac{1}{90}-\frac{8}{9}=\frac{-79}{90}\)
Tính tổng:\(S=\frac{1}{1\cdot3}-\frac{1}{2\cdot4}+\frac{1}{3\cdot5}-\frac{1}{4\cdot6}+\frac{1}{5\cdot7}-\frac{1}{6\cdot8}+\frac{1}{7\cdot9}-\frac{1}{8\cdot10}\)
Tính \(A=\left(\frac{1}{4\cdot9}+\frac{1}{9\cdot14}+\frac{1}{14\cdot19}+...+\frac{1}{44\cdot49}\right)\cdot\frac{1-3-5-7-...-49}{89}\)
\(B=\frac{5\cdot4^{15}\cdot9^9-4\cdot3^{20}\cdot8^9}{5\cdot2^{10}\cdot6^{19}-7\cdot2^{29}\cdot27^6}-\frac{2^{19}\cdot27^3+15\cdot4^9\cdot9^4}{6^9\cdot2^{10}+12^{10}}\)
tập hợp các số nguyên x thỏa mãn
\(x\cdot\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}\right)<1\frac{6}{7}\)
\(\frac{7}{3\cdot4}-\frac{9}{4\cdot5}+\frac{11}{5\cdot6}-\frac{13}{6\cdot7}+\frac{15}{7\cdot8}-\frac{17}{8\cdot9}+\frac{19}{9\cdot10}\)
\(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+..+\frac{1}{8\cdot9\cdot10}\cdot x=\frac{22}{45}\)thì x=
Tìm x biết: \(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{8\cdot9\cdot10}\cdot x=\frac{22}{45}\)Trình bày cách tính
tính:
\(\frac{1}{5\cdot6}-\frac{1}{6\cdot7}-\frac{1}{7\cdot8}-\frac{1}{8\cdot9}-...-\frac{1}{2004\cdot2005}\)
tìm x biết : (\(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+.....+\frac{1}{8\cdot9\cdot10}\)) x \(x=\frac{22}{45}\)
Tính A=\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+..........+\frac{1}{2017\cdot2018}\)
B=\(\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+..........+\frac{1}{2015\cdot2017}\)
C=\(\frac{1}{1\cdot4}+\frac{1}{4\cdot7}+\frac{1}{7\cdot10}+..........+\frac{1}{2017\cdot2020}\)
Ai làm nhanh nhất mình sẽ Tick cho nha.
