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Bài 2:
Ta thấy: 52 > 4.5
62 > 5.6
72 > 6.7
....
20172 > 2016.2017
\(\Rightarrow\)\(\frac{1}{5^2}< \frac{1}{4.5}\)
\(\frac{1}{6^2}< \frac{1}{5.6}\)
\(\frac{1}{7^2}< \frac{1}{6.7}\)
....
\(\frac{1}{2017^2}< \frac{1}{2016.2017}\)
Cộng vế với nhau, ta có:
\(\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{2017^2}\) < \(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{2016.2017}\)
\(\Rightarrow\)A < \(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{2016}-\frac{1}{2017}\)
\(\Rightarrow\)A < \(\frac{1}{4}-\frac{1}{2017}\)
\(\Rightarrow\)A < \(\frac{1}{4}\)( vì \(\frac{1}{2017}>0\))
k giúp mik ✅
BÀI 1
a, \(5\times\frac{-7}{10}=\frac{-35}{10}=\frac{-7}{2}\)
b, \(\frac{4}{5}\times\frac{-7}{10}=\frac{-28}{50}=\frac{-14}{25}\)
c, \(\frac{4}{9}+\frac{4}{3}\times\frac{16}{4}=\frac{4}{9}+\frac{16}{3}=\frac{52}{9}\)
d, \(\frac{11}{22}-\frac{3}{9}\times\frac{14}{21}=\frac{11}{22}-\frac{2}{9}=\frac{55}{198}=\frac{5}{18}\)
BÀI 2
\(A=\frac{6}{13}\times\frac{5}{7}+\frac{6}{13}\times\frac{2}{7}+\frac{17}{13}\)
\(A=\frac{30}{91}+\frac{12}{91}+\frac{17}{13}\)
\(A=\frac{30}{91}+\frac{12}{91}+\frac{119}{91}\)
\(A=\frac{161}{91}=\frac{23}{13}\)
\(B=\frac{11}{15}\times\frac{4}{11}+\frac{11}{15}\times\frac{5}{11}+\frac{11}{15}\times\frac{2}{11}\)
\(B=\frac{4}{15}+\frac{1}{3}+\frac{2}{15}\)
\(B=\frac{11}{15}\)
\(C=\left(\frac{19}{64}-\frac{33}{22}+\frac{24}{51}\right)\times\left(\frac{1}{5}-\frac{1}{15}-\frac{2}{15}\right)\)
\(C=\frac{-797}{1088}\times0\)
\(C=0\)
\(D=\frac{8}{13}\times\frac{7}{12}+\frac{8}{13}\times\frac{5}{12}-\frac{1}{12}\)
\(D=\frac{14}{39}+\frac{10}{39}-\frac{1}{12}\)
\(D=\frac{83}{156}\)
bạn biết câu náy không (24 + 11) . {546 - [14 . (64 - 2^{3}3) : 2]} =
\(-\frac{1}{10}< =x< =\frac{3}{5}\)
\(\frac{-4}{9}< x< =\frac{2}{3}\)
a)(-0,25).4/17.(-3 5/21).(-7/12)
= -1/17 . (-68/21) . ( -7/21)
= -4/63
b) (-2/5).4/15+(-3/10).4/15
= 4/15. [-2/5 + (-3/10)]
= 4/15 . (-7/10)
= -14/75
c)21-3 3/4:(3/8-1/6)
= 21 - 15/4 : 5/24
= 21 - 18
= 3
d) (-3/4+2/5):3/7+(3/5+-1/4):3/7
= [(-3/4 + 2/5) + (3/5 + -1/4)] : 3/7
= [-7/20 + (-17/20)] : 3/7
= -6/5 : 3/7
= -14/5
a) \(x=\dfrac{1}{4}+\dfrac{2}{13}\)
\(x=\dfrac{13}{52}+\dfrac{8}{52}\)
⇒ \(x=\dfrac{21}{52}\)
b) \(\dfrac{x}{3}=\dfrac{2}{3}+\dfrac{-1}{7}\)
\(\dfrac{x}{3}=\dfrac{14}{21}+\dfrac{-3}{21}\)
\(\dfrac{x}{3}=\dfrac{11}{21}\)
⇒ \(x=\dfrac{11.3}{21}=\dfrac{33}{21}\)
⇒ \(x=\dfrac{11}{7}\)
c) \(\dfrac{-8}{3}+\dfrac{1}{3}< x< \dfrac{-2}{7}+\dfrac{-5}{7}\)
\(\dfrac{-17}{7}< x< -1\)
⇒ \(-17< x< -7\)
⇒ \(x\in\left\{-16;-15,....;-6\right\}\)
d) \(\dfrac{1}{6}+\dfrac{2}{5}\)
\(=\dfrac{5}{30}+\dfrac{12}{30}\)
\(=\dfrac{17}{30}\)
e) \(\dfrac{3}{5}+\dfrac{-7}{4}\)
\(=\dfrac{12}{20}+\dfrac{-35}{20}\)
\(=\dfrac{-23}{20}\)
f) \(\dfrac{4}{13}+\dfrac{-12}{30}\)
\(=\dfrac{4}{13}+\dfrac{-2}{5}\)
\(=\dfrac{20}{65}+\dfrac{-26}{65}\)
\(=\dfrac{-6}{65}\)
g) \(\dfrac{-3}{29}+\dfrac{16}{58}\)
\(=\dfrac{-6}{58}+\dfrac{16}{58}\)
\(=\dfrac{10}{58}\)
h) \(\dfrac{8}{40}+\dfrac{-36}{45}\)
\(=\dfrac{1}{5}+\dfrac{-4}{5}\)
\(=\dfrac{-3}{5}\)
j) \(\dfrac{-8}{18}+\dfrac{15}{27}\)
\(=\dfrac{-2}{9}+\dfrac{5}{9}\)
\(=\dfrac{3}{9}\)
\(=\dfrac{1}{3}\)
dễ mk bn cho mình hỏi nhé câu 4 là \(\frac{1}{2\cdot3}\)hay là\(\frac{1}{2}\cdot3\)
\(A=\left(\frac{1}{3}-\frac{8}{15}-\frac{1}{7}\right)+\left[\frac{2}{3}-\left(-\frac{7}{15}\right)+\frac{8}{7}\right]\)
\(A=\frac{1}{3}-\frac{8}{15}-\frac{1}{7}+\frac{2}{3}+\frac{7}{15}+\frac{8}{7}\)
\(A=\left(\frac{1}{3}+\frac{2}{3}\right)+\left(-\frac{8}{15}+\frac{7}{15}\right)+\left(-\frac{1}{7}+\frac{8}{7}\right)\)
\(A=1+\left(-\frac{1}{15}\right)+1\)
\(A=\frac{29}{15}\)
\(B=\left[\left(0,25+\frac{3}{5}\right)-\left(\frac{1}{8}-\frac{2}{5}+\frac{5}{4}\right)\right]\)
\(B=\frac{1}{4}+\frac{3}{5}-\frac{1}{8}+\frac{2}{5}-\frac{5}{4}\)
\(B=\left(\frac{1}{4}-\frac{5}{4}\right)+\left(\frac{3}{5}+\frac{2}{5}\right)-\frac{1}{8}\)
\(B=-1+1-\frac{1}{8}\)
\(B=0-\frac{1}{8}\)
\(B=-\frac{1}{8}\)
\(=\frac{1}{3}-\frac{8}{15}-\frac{1}{7}+\frac{2}{3}+\frac{7}{15}+\frac{8}{7}\)
\(=\left(\frac{1}{3}+\frac{2}{3}\right)-\left(\frac{8}{15}+\frac{7}{15}\right)-\left(\frac{1}{7}-\frac{8}{7}\right)\)
\(=1-1+1\)
\(=0\)