A = \(\frac{1}{3}\left(\frac{3}{8.11}+\frac{3}{11.14}+.......+\frac{3}{605.608}\right)\)
= \(\frac{1}{3}\left(\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+......+\frac{1}{605}-\frac{1}{608}\right)\)
= \(\frac{1}{3}\left(\frac{1}{8}-\frac{1}{608}\right)=\frac{1}{3}.\frac{76-1}{608}=\frac{1}{3}.\frac{75}{608}=\frac{25}{608}\)
Tính tổng sau : \(A=\frac{1}{8\cdot11}+\frac{1}{11\cdot14}+...+\frac{1}{605\cdot608}\)
S= \(\frac{1}{2\cdot5}+\frac{1}{5\cdot8}+\frac{1}{8\cdot11}+\frac{1}{11\cdot14}+......+\frac{1}{97\cdot100}\)
Tìm x biết :
\(\frac{1}{5\cdot8}\)+\(\frac{1}{8\cdot11}\)+\(\frac{1}{11\cdot14}\)+ ... + \(\frac{1}{x\cdot\left(x+3\right)}\)=\(\frac{98}{1545}\)
\(\frac{3}{2\cdot5}+\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+\frac{3}{11\cdot14}+\frac{3}{14\cdot17}\)
Tính nhanh bằng cách thuận tiện nhất
a) 10,11+11,12+11,13+...+98,99+99,10
b) \(\frac{1}{1\cdot6}\cdot\frac{1}{6\cdot11}\cdot\frac{1}{11\cdot16}\cdot...\cdot\frac{1}{491\cdot496}\cdot\frac{1}{496\cdot501}\)
tính nhanh và ko quy đồng
a] C = \(\frac{5}{2\cdot1}+\frac{4}{1\cdot11}+\frac{3}{11\cdot2}+\frac{1}{2\cdot15}+\frac{13}{15\cdot4}\)
b] B = \(\frac{6}{3\cdot5}+\frac{6}{5\cdot7}+\frac{6}{7\cdot9}+.....+\frac{6}{97\cdot99}\)
Tính
\(\left(\frac{1}{3}+\frac{5}{6}\right)\cdot11-7\)
\(\frac{-5}{11}\cdot\frac{7}{15}\cdot\frac{11}{-5}\cdot\left(-30\right)\)
\(\frac{1}{10\cdot11}\)+\(\frac{1}{11\cdot12}\)+\(\frac{1}{12\cdot13}\)+ ......................+\(\frac{1}{49\cdot50}\)
A=\(\frac{\frac{6}{8}-\frac{6}{10}+\frac{6}{11}+\frac{6}{12}}{-0,625+\frac{1}{2}-\frac{5}{11}-\frac{5}{12}}\)
tính A
