\(A=\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+...+\dfrac{1}{2009\cdot2010}\\ =\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{2009}-\dfrac{1}{2010}\\ =\dfrac{1}{2}-\dfrac{1}{2010}< \dfrac{1}{2}\)\(B=\dfrac{1502}{3000}>\dfrac{1}{2}\)
\(\Rightarrow A< B\)
Tìm x biết:
a) \(\dfrac{x+5}{3}\)=\(\dfrac{x-6}{7}\)
b) x - \(\dfrac{20}{11.13}\)-\(\dfrac{20}{13.15}\)-\(\dfrac{20}{15.17}\)-...-\(\dfrac{20}{53.55}\)=\(\dfrac{3}{11}\)
\(\dfrac{1}{3}\)+\(\dfrac{1}{6}\)+\(\dfrac{1}{10}\)+...+\(\dfrac{2}{n\left(n+1\right)}\)=\(\dfrac{2015}{2016}\)
1.So Sánh
a) A=\(\dfrac{11}{2017}+\dfrac{4}{2019}và\) B=\(\dfrac{10}{2017}+\dfrac{10}{2019}\)
b) M=\(\dfrac{1}{5}+\dfrac{1}{12}+\dfrac{1}{13}+\dfrac{1}{14}+\dfrac{1}{30}+\dfrac{1}{61}+\dfrac{1}{62}và\dfrac{1}{2}\)
c) E=\(\dfrac{4116-14}{10290-35}và\) K=\(\dfrac{2929-101}{2.1919+404}\)
Bài 1: Thực hiện phép tính:
a, \(\left(\dfrac{7}{20}+\dfrac{11}{15}-\dfrac{15}{12}\right):\left(\dfrac{11}{20}-\dfrac{26}{45}\right)\)
b, \(\dfrac{5-\dfrac{5}{3}+\dfrac{5}{9}-\dfrac{5}{27}}{8-\dfrac{8}{3}+\dfrac{8}{9}-\dfrac{8}{27}}:\dfrac{15-\dfrac{15}{11}+\dfrac{15}{121}}{16-\dfrac{16}{11}+\dfrac{16}{121}}\)
c, \(\dfrac{\dfrac{1}{9}-\dfrac{5}{6}-4}{\dfrac{7}{12}-\dfrac{1}{36}-10}\)
a)Chứng minh \(\dfrac{1}{2}< \dfrac{1}{51}+\dfrac{1}{52}+\dfrac{1}{53}+..........+\dfrac{1}{100}< 1\)
b)So sánh A=\(\dfrac{10^{19}+1}{10^{20}+1}\) B=\(\dfrac{10^{20}+1}{10^{21}+1}\)
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, \(\dfrac{4}{3}+x\cdot\dfrac{2}{3}-\dfrac{1}{4}=4\dfrac{5}{12}\)
1. Tính giá trị của biểu thức :
a) ( 1 - \(\dfrac{1}{3}\) ) . ( 1- \(\dfrac{1}{6}\) ) . ( 1 - \(\dfrac{1}{10}\) ) ...... ( 1 - \(\dfrac{1}{780}\) )
b) \(\dfrac{2^4}{7.15}+\dfrac{2^4}{15.23}+\dfrac{2^4}{23.31}+.....+\dfrac{2^4}{55.63}-\dfrac{6.\left(-14\right)-17.\left(-7\right).\left(-2\right)}{-22.28}\)
2. Tìm số tự nhiên n biết : \(\dfrac{4}{3.5}+\dfrac{8}{5.9}+\dfrac{12}{9.15}+.....+\dfrac{32}{n.\left(n+16\right)}=\dfrac{16}{25}\)
3. So sánh A và B biết :
a) A = \(\dfrac{2003.2004-1}{2003.2004}\) và B = \(\dfrac{2004.2005-1}{2004.2005}\)
b) A = \(\dfrac{10^{25}+1}{10^{26}+1}\) và B = \(\dfrac{10^{26}+1}{10^{27}+1}\)
Hãy so sánh : \(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+...+\dfrac{1}{9900}\)với \(\dfrac{1}{2}\)
Tính giá trị của biểu thức:
B=\(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\)
Tính nhanh:
\(A=\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}\)
