a) A = \(\left(\dfrac{1}{1009}+\dfrac{1}{1010}+...+\dfrac{1}{2015}+\dfrac{1}{2016}\right):\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+...\dfrac{1}{2015}-\dfrac{1}{2016}\right)\)
b) B = \(\dfrac{5x^2+3y^2}{10x^2-3y^2}\) biết \(\dfrac{x}{3}=\dfrac{y}{5}\)
\(\dfrac{x+1}{2014}+\dfrac{x+2}{2013}=...+\dfrac{x+1007}{1008}=\dfrac{x+1008}{1007}+\dfrac{x+1009}{1006}+...+\dfrac{x+2014}{1}\)
1, Tính:
a, A = \(\dfrac{24.47-23}{24.47-23}\).\(\dfrac{3.\dfrac{3}{7}-\dfrac{3}{31}+\dfrac{3}{1001}-\dfrac{3}{13}}{\dfrac{9}{1001}-\dfrac{9}{15}+\dfrac{9}{7}-\dfrac{9}{11}+9}\)
b, B = 1 + 2 + 2\(^2\) + 2\(^3\) + .....+ 2 \(^{2013}\)
1.Tính
a) (\(\dfrac{-2}{3}\)+1\(\dfrac{1}{4}\)-\(\dfrac{1}{6}\)).\(\dfrac{-24}{10}\)
b) \(\dfrac{13}{15}\).0,25.3+(\(\dfrac{8}{15}\)-\(1\dfrac{19}{60}\)):\(1\dfrac{23}{24}\)
c) (\(\dfrac{12}{32}\)+\(\dfrac{5}{-20}\)-\(\dfrac{10}{24}\)):\(\dfrac{2}{3}\)
d) \(4\dfrac{1}{2}\):(2,5-\(3\dfrac{3}{4}\))+(\(\dfrac{-1}{2}\))\(^2\)
e) \(\dfrac{-5}{2}\):(\(\dfrac{3}{4}\)-\(\dfrac{1}{2}\))
2. Tính nhanh
a) \(\dfrac{5}{23}\).\(\dfrac{17}{26}\)+\(\dfrac{5}{23}\).\(\dfrac{10}{26}\)-\(\dfrac{5}{23}\)
b) \(\dfrac{1}{7}\).\(\dfrac{5}{9}\)+\(\dfrac{5}{9}\).\(\dfrac{2}{7}\)+\(\dfrac{5}{9}\).\(\dfrac{1}{7}\)+\(\dfrac{5}{9}\).\(\dfrac{3}{7}\)
Bài 2 Tính nhanh
a) \(\dfrac{5}{23}\) x \(\dfrac{17}{26}\) + \(\dfrac{5}{23}\) x \(\dfrac{10}{26}\) - \(\dfrac{5}{23}\)
b) \(\dfrac{1}{7}\) x \(\dfrac{5}{9}\) + \(\dfrac{5}{9}\) x \(\dfrac{2}{7}\) + \(\dfrac{5}{9}\) x \(\dfrac{1}{7}\) + \(\dfrac{5}{9}\) x \(\dfrac{3}{7}\)
BT1: Tính nhanh:
1) (\(\dfrac{12}{23}+\dfrac{12}{2323}-\dfrac{121212}{232323}\)) . ( \(\dfrac{1}{3}+\dfrac{1}{4}\) - \(\dfrac{7}{12}\))
Tính giá trị biểu thức :
\(\dfrac{1}{2}-\left(\dfrac{1}{3}+\dfrac{2}{3}\right)+\left(\dfrac{1}{4}+\dfrac{2}{4}+\dfrac{3}{4}\right)-\left(\dfrac{1}{5}+\dfrac{2}{5}+\dfrac{3}{5}+\dfrac{4}{5}\right)+\left(\dfrac{1}{6}+\dfrac{2}{6}+\dfrac{3}{6}+\dfrac{4}{6}+\dfrac{5}{6}\right)-\left(\dfrac{1}{7}+\dfrac{2}{7}+\dfrac{3}{7}+\dfrac{4}{7}+\dfrac{5}{7}+\dfrac{6}{7}\right)+...+\left(100+...+\dfrac{99}{100}\right)\)
bài 1: TÍNH HỢP LÝ
a, \(49\dfrac{8}{23}-\left(5\dfrac{7}{32}+14\dfrac{8}{23}\right)\)
b, \(-\dfrac{3}{7}.\dfrac{5}{9}+\dfrac{4}{9}.\dfrac{-3}{7}+2\dfrac{3}{7}\)
c, \(0,7.2\dfrac{2}{3}.20.0.375.\dfrac{5}{28}\)
d, \(\left(9\dfrac{30303}{80808}+7\dfrac{303030}{484848}\right)+4.03\)
Cho A=1-\(\dfrac{1}{2}\)+\(\dfrac{1}{3}\)-\(\dfrac{1}{4}\)+...+\(\dfrac{1}{2016}\)+\(\dfrac{1}{2017}\)
Chứng minh A=\(\dfrac{1}{1009}\)+\(\dfrac{1}{1010}\)+\(\dfrac{1}{1001}\)+\(\dfrac{1}{2017}\)
help me