Bài 1:Tính
a, A=\(\dfrac{3}{4}\cdot\dfrac{8}{9}\cdot\dfrac{15}{16}\cdot....\cdot\dfrac{9999}{10000}\)
b,B=\(\left(1-\dfrac{1}{21}\right)\cdot\left(1-\dfrac{1}{28}\right)\cdot\left(1-\dfrac{1}{36}\right)\cdot....\cdot\left(1-\dfrac{1}{1326}\right)\)
c,C=\(\left(1+\dfrac{1}{1\cdot3}\right)\cdot\left(1+\dfrac{1}{2\cdot4}\right)\cdot\left(1+\dfrac{1}{3\cdot5}\right)\cdot....\cdot\left(1+\dfrac{1}{99\cdot101}\right)\)
\(A=\left(1-\dfrac{1}{2}\right)\cdot1-\dfrac{1}{3}\cdot......\cdot\left(1-\dfrac{1}{2016}\right)\cdot\left(1-\dfrac{1}{2017}\right)\)
\(\dfrac{-5}{9}+1\dfrac{5}{9}\cdot\left(\dfrac{3}{4}-\dfrac{2}{5}\right):7^2\)
\(1\dfrac{13}{15}\cdot0,75-\left(\dfrac{104}{195}+25\%\right)\cdot\dfrac{24}{47}-3\dfrac{12}{13}:3\)
\(1\dfrac{13}{15}\cdot\left(0,5\right)^2\cdot3+\left(\dfrac{8}{15}+1\dfrac{19}{60}\right):1\dfrac{23}{24}\)
2.Tính:
A=\(\left(\dfrac{1}{10}-1\right).\left(\dfrac{1}{11}-1\right)\left(\dfrac{1}{12}-1\right).....\left(\dfrac{1}{100}-1\right)\)
B=\(\left(1-\dfrac{1}{2^2}\right)\left(1-\dfrac{1}{3^2}\right)\left(1-\dfrac{1}{10^2}\right)\)
C=\(\left(\dfrac{7}{9}+1\right)\left(\dfrac{7}{20}+1\right)\left(\dfrac{7}{33}+1\right)...\left(\dfrac{7}{108080}+1\right)\)
D=\(\left(1-\dfrac{28}{10}\right)\left(1-\dfrac{52}{22}\right)\left(1-\dfrac{80}{36}\right)...\left(1-\dfrac{21808}{10900}\right)\)
1. Tìm X
a, \(\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}\right)\cdot10-x=0\)
b, \(\left(\dfrac{1}{11}-\dfrac{1}{21}\right)\cdot462-2.04:\left(x+1.5\right)+11.02=30\)
c, \(\dfrac{4}{3}+x\cdot\dfrac{2}{3}-\dfrac{1}{4}=4\dfrac{5}{12}\)
tính tổng
S=\(\dfrac{1}{1\cdot2\cdot3}+\dfrac{1}{2\cdot3\cdot4}+\dfrac{1}{3\cdot4\cdot5}+...+\dfrac{1}{n\cdot\left(n+1\right)\cdot\left(n+2\right)}\)
A=1+\(\dfrac{1}{3}+\dfrac{1}{5}+\dfrac{1}{7}+...+\dfrac{1}{99}\)
B= \(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...\dfrac{1}{100}\)
C=\(\dfrac{99}{1}+\dfrac{98}{2}+\dfrac{97}{3}+...+\dfrac{1}{99}\)
c) \(\left(6-\dfrac{14}{5}\right)\cdot\dfrac{25}{8}-\dfrac{18}{5}\cdot\dfrac{1}{4}\)
Tìm x biết \(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+....\dfrac{2}{x\cdot\left(x+1\right)}=\dfrac{2014}{2016}\)
BT2: Tính nhanh
7) \(\left(-\dfrac{1}{2}\right)-\left(-\dfrac{3}{5}\right)+\left(-\dfrac{1}{9}\right)+\dfrac{1}{71}-\left(-\dfrac{2}{7}\right)+\dfrac{4}{35}-\dfrac{7}{18}\)
8)\(\left(3-\dfrac{1}{4}+\dfrac{2}{3}\right)-\left(5-\dfrac{1}{3}-\dfrac{6}{5}\right)-\left(6-\dfrac{7}{4}+\dfrac{3}{2}\right)\)
