a) \(D=\dfrac{1}{2}-\dfrac{1}{2^4}+\dfrac{1}{2^7}-\dfrac{1}{2^{10}}+...-\dfrac{1}{2^{58}}\)
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VV
2
LG
23 tháng 7 2017
Sửa đề: \(A=\dfrac{1}{2}+\dfrac{1}{2^4}+\dfrac{1}{2^7}+....+\dfrac{1}{2^{58}}\)
Ta có : \(A=\dfrac{1}{2}+\dfrac{1}{2^4}+\dfrac{1}{2^7}+.....+\dfrac{1}{2^{58}}\)
\(\Rightarrow2^3A=2^3.\left(\dfrac{1}{2}+\dfrac{1}{2^4}+\dfrac{1}{2^7}+\dfrac{1}{2^{58}}\right)\)
\(\Rightarrow2^3A=1+\dfrac{1}{2}+\dfrac{1}{2^4}+.....+\dfrac{1}{2^{55}}\)
\(\Rightarrow2^3A-A=\left(1+\dfrac{1}{2}+\dfrac{1}{2^4}+\dfrac{1}{2^7}+...+\dfrac{1}{2^{55}}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^7}+....+\dfrac{1}{2^{58}}\right)\)\(\Rightarrow7A=1-\dfrac{1}{2^{58}}\Rightarrow A=\dfrac{1-\dfrac{1}{2^{58}}}{7}\)
Vậy...........
~ Học tốt nha ~
MV
23 tháng 7 2017
\(A=\dfrac{1}{2}+\dfrac{1}{2^4}+\dfrac{1}{2^7}+...+\dfrac{1}{2^{58}}\\ 2^3\cdot A=\dfrac{2^3}{2}+\dfrac{2^3}{2^4}+\dfrac{2^3}{2^7}+...+\dfrac{2^3}{2^{58}}\\ 8A=4+\dfrac{1}{2}+\dfrac{1}{2^4}+...+\dfrac{1}{2^{55}}\\ 8A-A=\left(4+\dfrac{1}{2}+\dfrac{1}{2^4}+...+\dfrac{1}{2^{55}}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^4}+\dfrac{1}{2^7}+...+\dfrac{1}{2^{58}}\right)\\ 7A=4-\dfrac{1}{2^{58}}\\ A=\dfrac{4-\dfrac{1}{2^{58}}}{7}\)
25 tháng 3 2022
\(\dfrac{1}{5}+\dfrac{2}{11}< \dfrac{x}{55}< \dfrac{2}{5}+\dfrac{1}{5}\)
\(\dfrac{11+10}{55}< \dfrac{x}{55}< \dfrac{3}{5}\)
\(\dfrac{21}{55}< \dfrac{x}{55}< \dfrac{33}{55}\)
Vậy \(x\in\left\{22;23;24;...\right\}\)
KT
9 tháng 4 2022
a: x=4/27-2/3=4/27-18/27=-14/27
b: =>3/4x-1/4x=1/6+7/3
=>1/2x=1/6+14/6=5/2
hay x=5
c: =>13/10x=7/2+5/2=6
=>x=13/10:6=13/60
d: (3x+2)(-2/5x-7)=0
=>3x+2=0 hoặc 2/5x+7=0
=>x=-2/3 hoặc x=-35/2
MN
17 tháng 7 2021
a) \(1-\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{6}{6}-\dfrac{3}{6}+\dfrac{2}{6}=\dfrac{6-3+2}{6}=\dfrac{1}{6}\)
\(b.\) \(\dfrac{2}{5}+\dfrac{3}{5}:\dfrac{9}{10}=\dfrac{2}{5}+\dfrac{3}{5}.\dfrac{10}{9}=\dfrac{2}{5}+\dfrac{2}{3}=\dfrac{6}{15}+\dfrac{10}{15}=\dfrac{6+10}{15}=\dfrac{16}{15}\)
\(c.\) \(\dfrac{7}{11}.\dfrac{3}{4}+\dfrac{7}{11}.\dfrac{1}{4}+\dfrac{4}{11}=\dfrac{21}{44}+\dfrac{7}{44}+\dfrac{4}{11}=\dfrac{21}{44}+\dfrac{7}{44}+\dfrac{16}{44}=\dfrac{21+7+16}{44}=\dfrac{44}{44}=1\)
17 tháng 7 2021
a/\(1-\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{6}{6}-\dfrac{3}{6}+\dfrac{2}{6}=\dfrac{5}{6}\)
b/\(\dfrac{2}{5}+\dfrac{3}{5}:\dfrac{9}{10}=\dfrac{2}{5}+\dfrac{3}{5}.\dfrac{10}{9}=\dfrac{2}{5}+\dfrac{2}{3}=\dfrac{6}{15}+\dfrac{10}{15}=\dfrac{16}{15}\)
26 tháng 7 2021
a) \(\dfrac{-12}{15}+\dfrac{-4}{26}=\dfrac{-4}{5}+\dfrac{-2}{13}=\dfrac{-52-10}{65}=\dfrac{-62}{65}\)
b) \(5\dfrac{1}{3}-2\dfrac{4}{5}=\dfrac{16}{3}-\dfrac{14}{5}=\dfrac{80}{15}-\dfrac{42}{15}=\dfrac{38}{15}\)
c) \(\dfrac{4}{5}-\left(-\dfrac{2}{7}\right)+\dfrac{-5}{10}=\dfrac{4}{5}+\dfrac{2}{7}-\dfrac{1}{2}=\dfrac{56}{70}+\dfrac{20}{70}-\dfrac{35}{70}=\dfrac{41}{70}\)
d) \(-1\dfrac{2}{7}+\dfrac{3}{14}-\dfrac{5}{21}=\dfrac{-9}{7}+\dfrac{3}{14}-\dfrac{5}{21}=\dfrac{-54}{42}+\dfrac{9}{42}-\dfrac{10}{42}=\dfrac{-55}{42}\)
e) \(12-\dfrac{11}{121}+\left(\dfrac{-8}{9}\right)-\left(-\dfrac{3}{7}\right)\)
\(=12-\dfrac{11}{121}-\dfrac{8}{9}+\dfrac{3}{7}\)
\(=\dfrac{91476}{7623}-\dfrac{693}{7623}-\dfrac{6776}{7623}+\dfrac{3267}{7623}\)
\(=\dfrac{7934}{693}\)
K
7 tháng 4 2022
\(a,\dfrac{13}{14}\cdot\dfrac{-7}{8}+\dfrac{-3}{2}\)
\(=-\dfrac{13}{16}+\dfrac{-3}{2}\)
\(=-\dfrac{13}{16}+\dfrac{-24}{16}\)
\(=-\dfrac{37}{16}\)
\(b,\dfrac{5}{17}+\dfrac{-15}{34}\cdot\dfrac{2}{5}\)
\(=\dfrac{5}{17}+\dfrac{-3}{17}\)
\(=\dfrac{2}{17}\)
\(c,\dfrac{1}{5}:\dfrac{1}{10}-\dfrac{1}{3}\cdot\left(\dfrac{6}{5}-\dfrac{2}{4}\right)\)
\(=2-\dfrac{1}{3}\cdot\dfrac{7}{10}\)
\(=2-\dfrac{7}{30}\)
\(=\dfrac{53}{30}\)
\(d,\dfrac{-3}{4}:\left(\dfrac{12}{-5}-\dfrac{-7}{10}\right)\)
\(=\dfrac{-3}{4}:\dfrac{-17}{10}\)
\(=\dfrac{15}{34}\)
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