Cho:
\(A=\frac{1.11+0.19-1.3\cdot2}{2.06+0.54}-\left(\frac{1}{2}+\frac{1}{3}\right)\div2\)2
\(B=\left(5\frac{7}{8}-2\frac{1}{4}-0.5\right)\div2\frac{23}{26}\)
a. Rút gọn A và B b. Tìm \(x\in Z\)để A<x<B
cho:
\(A=\frac{1}{2}+\frac{3}{2}+\left(\frac{3}{2}\right)^2+\left(\frac{3}{2}\right)^3+...+\left(\frac{3}{2}\right)^{2012}\)
và \(B=\left(\frac{3}{2}\right)^{2013}\div2\)
tính B - A
\(A=\frac{1}{2}+\frac{3}{2}+\left(\frac{3}{2}\right)^2+\left(\frac{3}{2}\right)^3+...+\left(\frac{3}{2}\right)^{2012}\)(1)
\(\frac{3}{2}A=\frac{3}{4}+\left(\frac{3}{2}\right)^2+\left(\frac{3}{2}\right)^3+\left(\frac{3}{2}\right)^4+...+\left(\frac{3}{2}\right)^{2013}\)(2)
Lấy (2) trừ (1) ta được:
\(\frac{1}{2}A=\frac{3}{4}+\left(\frac{3}{2}\right)^{2013}-\frac{1}{2}-\frac{3}{2}=\left(\frac{3}{2}\right)^{2013}-\frac{5}{4}\)
\(A=\frac{\left(\frac{3}{2}\right)^{2013}-\frac{5}{4}}{\frac{1}{2}}=\left(\frac{3}{2}\right)^{2013}.2-\frac{5}{4}.2=\left(\frac{3}{2}\right)^{2013}.2-\frac{5}{2}\)
\(\Rightarrow B-A=\left(\frac{3}{2}\right)^{2013}\cdot\frac{1}{2}-\left(\frac{3}{2}\right)^{2013}.2+\frac{5}{2}=-\left(\frac{3}{2}\right)^{2014}+\frac{5}{2}\)
A= \(-1,6\div\left(1+\frac{2}{3}\right)\)
B=\(1,4\times\frac{15}{49}-\left(\frac{4}{5}+\frac{2}{3}\right)\div2\frac{1}{5}\)
\(A=-1,6:\left(1+\frac{2}{3}\right)\)
\(A=-\frac{16}{10}:\frac{5}{3}\)
\(A=-\frac{16.3}{10.5}=-\frac{48}{50}=-\frac{24}{25}\)
\(B=1,4\times\frac{15}{49}-\left(\frac{4}{5}+\frac{2}{3}\right):2\frac{1}{5}\)
\(B=\frac{14}{10}\times\frac{15}{49}-\left(\frac{4}{5}+\frac{2}{3}\right):\frac{11}{5}\)
\(B=\frac{2.7.3.5}{2.5.7.7}-\left(\frac{12+10}{15}\right):\frac{11}{5}\)
\(B=\frac{3}{7}-\frac{22}{15}:\frac{11}{5}\)
\(B=\frac{3}{7}-\frac{22}{15}\times\frac{5}{11}=\frac{3}{7}-\frac{2.11.5}{3.5.11}\)
\(B=\frac{3}{7}-\frac{2}{3}=\frac{9-14}{21}=-\frac{5}{21}\)
Ủng hộ mk nha !!! ^_^
\(A=\frac{1,31+0,19-13,2}{2,06+0,54}-\left(\frac{1}{2}+\frac{1}{4}\right):2\)2
\(B=\left(5\frac{7}{8}-2\frac{1}{4}-0,5\right):2\frac{23}{26}\)
a) Rút gọn A và B
b) Tìm x thuộc Z để A<x<B
Cho \(A=\frac{1,11+0,19-13.2}{2,06+0,54}-\left(\frac{1}{2}+\frac{1}{4}\right):2\)
\(B=\left(5\frac{7}{8}-2\frac{1}{4}-0,5\right):2\frac{23}{26}\)
a)Rút gọn A , B
b)Tìm x thuộc Z để A<x<B
Cho \(A=\frac{1,11+0,19-13.2}{2,06+0,54}-\left(\frac{1}{2}+\frac{1}{4}\right):2\)
\(B=\left(5\frac{7}{8}-2\frac{1}{4}-0,5\right):2\frac{23}{26}\)
a)Rút gọn A,B
b)Tìm x thuộc Z để A<x<B
a: \(A=\dfrac{1.3-26}{2.6}-\dfrac{3}{8}\cdot\dfrac{1}{2}=-\dfrac{19}{2}-\dfrac{3}{16}=-\dfrac{155}{16}\)
b: \(B=\left(\dfrac{47}{8}-\dfrac{9}{4}-\dfrac{1}{2}\right):\dfrac{75}{26}\)
\(=\dfrac{47-18-4}{8}\cdot\dfrac{26}{75}=\dfrac{1}{3}\cdot\dfrac{13}{4}=\dfrac{13}{12}\)
c: Để A<x<B thì \(-\dfrac{155}{16}< x< \dfrac{13}{12}\)
=>-10<x<2
hay \(x\in\left\{-9;-8;-7;...;0;1\right\}\)
Tính giá trị biểu thức sau:
B = \(\left(-13\cdot\frac{2}{5}+\frac{-2}{9}\div2\frac{1}{2}+\frac{2}{5}\cdot\frac{11}{9}\right)\cdot2\frac{1}{2}\)
\(B=\left(-13\cdot\frac{2}{5}+\frac{-2}{9}\div2\frac{1}{2}+\frac{2}{5}\cdot\frac{11}{9}\right)\cdot2\frac{1}{2}\)
\(B=\left(13\cdot\frac{2}{5}+\frac{-2}{9}\cdot\frac{2}{5}+\frac{2}{5}\cdot\frac{11}{9}\right)\cdot\frac{5}{2}\)
\(B=\left[\frac{2}{5}\cdot\left(-13+\frac{-2}{9}+\frac{11}{9}\right)\right]\cdot\frac{5}{2}\)
\(B=\left[\frac{2}{5}\cdot\left(-12\right)\right]\cdot\frac{5}{2}\)
\(B=\frac{-24}{5}\cdot\frac{5}{2}=-12\)
Rút gọn:
a,\(A=\frac{5\cdot4^{15}\cdot9^9-4\cdot3^{20}\cdot8^9}{5\cdot2^9\cdot6^{19}-7\cdot2^{29}\cdot27^6}\)
b,\(B=\left(1+\frac{1}{1\cdot3}\right)\left(1+\frac{1}{2\cdot4}\right)\left(1+\frac{1}{3\cdot5}\right)...\left(1+\frac{1}{2014\cdot2016}\right)\)
Rút gọn biểu thức sau:
P=\(\frac{\left(\frac{13}{84}\times1,4-2,5\times\frac{7}{180}\right)\div2\frac{7}{18}+4\frac{1}{2}\times0,1}{70,7-528:\frac{7}{1}}\)
cho A=\(\frac{1,1+0,19-1,3\times2}{2,06+0,54}-\left(\frac{1}{2}+\frac{1}{3}\right):2\)
B=\(\left(5\frac{7}{8}-2\frac{1}{2}-0,5\right):2\frac{23}{26}\)
a. Rút gọn A
b. Tim x \(\in\)Z để A<x<B