\(tuA=1003+1007+\dfrac{2010}{113}+\dfrac{2010}{117}-\dfrac{2010}{119}=2010\left(1+\dfrac{1}{113}+\dfrac{1}{117}-\dfrac{1}{119}\right)\)\(mauA=1003+1008+\dfrac{2011}{113}+\dfrac{2011}{117}-\dfrac{2011}{119}=2011\left(1+\dfrac{1}{113}+\dfrac{1}{117}-\dfrac{1}{119}\right)\)có \(\left(1+\dfrac{1}{113}+\dfrac{1}{117}-\dfrac{1}{119}\right)\ne0=>A=\dfrac{2010}{2011}\)
Tính tổng :
a) B = \(\dfrac{1}{5}\) + \(\dfrac{1}{20}\)+ \(\dfrac{1}{44}\) +\(\dfrac{1}{77}\) +\(\dfrac{1}{119}\) + \(\dfrac{1}{170}\) +\(\dfrac{1}{230}\) +\(\dfrac{1}{299}\)
b) C = \(\left(1+\dfrac{1}{1.3}\right)\) \(\left(1+\dfrac{1}{2.4}\right)\) \(\left(1+\dfrac{1}{3.5}\right)\) .....\(\left(1+\dfrac{1}{2014.2016}\right)\)
1,so sánh A và B biết:A=\(\dfrac{2010}{2011}+\dfrac{2011}{2012}+\dfrac{2012}{2010};B=\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+...+\dfrac{1}{17}\)
Bài 2 : So sánh
\(A=\dfrac{2008}{2009}+\dfrac{2009}{2010}+\dfrac{2010}{2011}vàB=\dfrac{2008+2009+2010}{2009+2010+2011}\)
1,
a,tính:\(\dfrac{\dfrac{7}{2012}+\dfrac{7}{9}-\dfrac{1}{4}}{\dfrac{5}{9}-\dfrac{1}{2012}-\dfrac{1}{2}}\)
b,so sánh:A=\(\dfrac{2010}{2011}+\dfrac{2011}{2012}+\dfrac{2012}{2010};B=\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+...+\dfrac{1}{17}\)
Tìm x biết \(\left(\dfrac{1}{1.2.3.4}+\dfrac{1}{2.3.4.5}+\dfrac{1}{3.4.5.6}+...+\dfrac{1}{7.8.9.10}\right).x=\dfrac{119}{720}\)
Không quy đồng phân số, hãy so sánh: A = \(\dfrac{-9}{10^{2010}}+\dfrac{-19}{10^{2011}}\)và B = \(\dfrac{-9}{10^{2011}}+\dfrac{-19}{10^{2010}}\)
Rút gọn phân số:
a) \(\dfrac{2929-101}{2.1149+404}\)
b) \(\dfrac{6.9-2.17}{63.3-119}\)
c) \(\dfrac{3.13-13.18}{15.40-80}\)
d) \(\dfrac{-1997-1996+1}{\left(-1995\right).\left(-1997\right)+1996}\)
e) \(\dfrac{2.3+4.6+14.21}{3.5+6.10+21.35}\)
g) \(\dfrac{\left(-5\right)^3.40.4^3}{135.\left(-3\right)^{14}.\left(-100\right)^0}\)
h) \(\dfrac{18.34+\left(-18\right).124}{-36.17+9.\left(52\right)}\)
j) \(\dfrac{9.11+32.9}{23.15+12.23}\)
k) \(\dfrac{12.13+24.26+36.39}{24.26+48.52+72.78}\)
Câu 3:
a)\(2^x+2^{x+1}+2^{x+2}+2^{x+3}=480\)
b)\(\left(\dfrac{1}{2}+\dfrac{1}{3}+.....+\dfrac{1}{2013}+\dfrac{1}{2013}\right).x=\dfrac{2012}{1}+\dfrac{2011}{2}+\dfrac{2010}{3}+.....+\dfrac{2}{2011}+\dfrac{1}{2012}\)
1 So sánh
a) \(\dfrac{51}{56}và\dfrac{61}{66}\)
b)\(\dfrac{41}{43}và\dfrac{172}{165}\)
c)\(\dfrac{101}{506}và\dfrac{-707}{3534}\)
d) \(\dfrac{-43}{119}và\dfrac{41}{117}\)
2 Rút gọn và quy đồng
a)\(\dfrac{125}{1000};\dfrac{198}{126};\dfrac{3}{243};\dfrac{103}{3009}\)
b)\(\dfrac{1}{2};\dfrac{1}{3};\dfrac{1}{38};\dfrac{-1}{12}\)
c)\(\dfrac{9}{30};\dfrac{90}{8};\dfrac{15}{1000}\)
3 So sánh
a)\(\dfrac{-3}{5}và\dfrac{39}{65}\)
b)\(\dfrac{-9}{27}và\dfrac{11}{123}\)
c) \(\dfrac{-3}{4}và\dfrac{4}{-5}\)
d)\(\dfrac{2}{-3}và\dfrac{5}{7}\)
