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a) Đặt A=1/2 + 1/4 + 1/8 +...+ 1/256 + 1/512
\(A=\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\)
\(2A=1+\frac{1}{2}+...+\frac{1}{2^8}\)
\(2A-A=\left(1+\frac{1}{2}+...+\frac{1}{2^8}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\right)\)
\(A=1-\frac{1}{2^9}\)
b)\(\frac{a}{b}+\frac{4}{6}+\frac{2}{10}=\frac{3}{2}\)
\(\Rightarrow\frac{a}{b}+\frac{13}{15}=\frac{3}{2}\)
\(\Rightarrow\frac{a}{b}=\frac{19}{30}\)
\(\frac{4}{5}:\frac{a}{b}-\frac{6}{5}=\frac{3}{10}\)
\(\Rightarrow\frac{4}{5}:\frac{a}{b}=\frac{3}{2}\)
\(\Rightarrow\frac{a}{b}=\frac{8}{15}\)
Bài 1:
a) \(\dfrac{-5}{6}\ne\dfrac{10}{-14}\left(\dfrac{10}{-14}=-\dfrac{5}{7}\right).\)
b) \(\dfrac{-15}{-60}\ne\dfrac{-3}{12}\left(\dfrac{-15}{-60}=\dfrac{1}{4}\right).\)
Bài 2:
a) \(\dfrac{20}{-140}=-\dfrac{1}{7}.\)
b) \(\dfrac{4.18}{9.12}=\dfrac{72}{108}=\dfrac{2}{3}.\)
c) \(\dfrac{17.25-17.3}{2.\left(-15\right)}=\dfrac{17.\left(25-3\right)}{-30}=-\dfrac{17.22}{30}=\dfrac{374}{30}=\dfrac{187}{15}.\)
Bài 3:
a) \(\dfrac{-3}{5}< \dfrac{4}{-7}.\)
b) \(\dfrac{-4}{21}>\dfrac{-7}{35}.\)
c) \(\dfrac{-7}{24}>\dfrac{-2}{3}.\)
d) \(\dfrac{-52}{167}< \dfrac{-3}{-4}.\)
a) \(\frac{3}{-4}=\frac{-3}{4};\frac{-1}{-4}=\frac{1}{4}\)
Vì - 3 < 1 nên \(\frac{-3}{4}< \frac{1}{4}\)
hay \(\frac{3}{-4}< \frac{-1}{-4}\)
Quy đồng mẫu ta được:
15/17=15.27/17.27=405/459
25/27=25.17/27.27=425/459
⇒405/459<425/459⇒15/17<25/27
Ta có:\(\frac{3}{15}=\frac{3.2}{15.2}\)
\(\Rightarrow\frac{3}{15}=\frac{1}{5}\)
\(\Rightarrow\frac{6}{18}=\frac{1}{3}\)
\(\Rightarrow\frac{3}{15}< \frac{6}{18}\)
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Bài 3:
a: \(\dfrac{3}{5}-x=\dfrac{-1}{4}+\dfrac{7}{10}=\dfrac{-5}{20}+\dfrac{14}{20}=\dfrac{9}{20}\)
=>x=3/5-9/20=12/20-9/20=3/20
b: \(\dfrac{-5}{-8}-x=\dfrac{-5}{-6}+\dfrac{1}{8}\)
=>5/8-x=5/6+1/8
=>5/8-x=23/24
=>x=-1/3
c: \(8.25-x=3+\dfrac{1}{6}=\dfrac{19}{6}\)
=>x=33/4-19/6=99/12-38/12=61/12
a) − 1 2 > − 7 12
b) 71 20 < 4