\(\dfrac{1}{9}+\dfrac{1}{10}< \dfrac{1}{8}+\dfrac{1}{8}=\dfrac{1}{4}\) và \(\dfrac{1}{41}+\dfrac{1}{42}< \dfrac{1}{40}+\dfrac{1}{40}=\dfrac{1}{20}\)
Suy ra:
\(S=\dfrac{1}{5}+\dfrac{1}{9}+\dfrac{1}{10}+\dfrac{1}{41}+\dfrac{1}{42}< \dfrac{1}{5}+\dfrac{1}{4}+\dfrac{1}{20}=\dfrac{1}{2}\)
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)\(\dfrac{2}{-3}và\dfrac{5}{7}\)
Tính nhanh :
\(C=\dfrac{1}{3}+\dfrac{-3}{4}+\dfrac{3}{5}+\dfrac{1}{57}+\dfrac{-1}{36}+\dfrac{1}{15}+\dfrac{-2}{9}\)
\(D=\dfrac{1}{2}+\dfrac{-1}{5}+\dfrac{-5}{7}+\dfrac{1}{6}+\dfrac{-3}{35}+\dfrac{1}{3}+\dfrac{1}{41}\)
\(E=\dfrac{-1}{2}+\dfrac{3}{5}+\dfrac{-1}{9}+\dfrac{1}{127}+\dfrac{-7}{18}+\dfrac{4}{35}+\dfrac{2}{7}\)
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=\(\dfrac{2010}{2011}+\dfrac{2011}{2012}+\dfrac{2012}{2010};B=\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+...+\dfrac{1}{17}\)
Bài1. (4điểm) Thực hiện phép tính:
a) \(A=\dfrac{3}{5}+6\dfrac{5}{6}\left(11\dfrac{5}{20}-9\dfrac{1}{4}\right):8\dfrac{1}{3}\)
b) \(B=\dfrac{-1}{2}+\dfrac{-1}{6}+\dfrac{-1}{12}+\dfrac{-1}{20}+\dfrac{-1}{30}+\dfrac{-1}{42}+\dfrac{-1}{56}+\dfrac{-1}{72}+\dfrac{-1}{90}\)
\(S=\dfrac{2}{2021+1}+\dfrac{2^2}{2021^2+1}+\dfrac{2^3}{2021^{2^2}+1}+...+\dfrac{2^{n+1}}{2021^{2^n}+1}+...+\dfrac{2^{2021}}{2021^{2^{2020}}+1}\)
So sánh S với \(\dfrac{1}{1010}\)
So sánh giá trị 2 biểu thức:
A=\(\dfrac{1+7+7^2+...+7^9}{1+7+7^2+...+7^{10}}\) và B=\(\dfrac{1+5+5^2+...+5^9}{1+5+5^2+...+5^{10}}\)
Mí bạn giúp tớ điii
giải rõ hộ nha :3
So sánh A và B :
\(A=\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{100}}\)
\(B=\dfrac{1}{2}\)
so sánh \(\dfrac{1}{2^{500}}\) và \(\dfrac{1}{5^{200}}\)
Cho biểu thức
\(A=\dfrac{-10}{52}+\dfrac{-10}{140}+\dfrac{-10}{260}+...+\dfrac{-10}{140}\)
so sánh A với \(\dfrac{-1}{3}\)
Tính giá trị biểu thức
B=\(2013+\dfrac{2013}{1+2}+\dfrac{2013}{1+2+3}+\dfrac{2013}{1+2+3+4}+...+\dfrac{2013}{1+2+3+4+5}\)
