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LT
3
29 tháng 4 2015
Ta có:
(1/2 + 1/4 + 1/8 + 1/16) = 8/16 + 4/16 + 2/16 + 1/16 = 15/16.
1/2 + 1/6 + 1/12 + 1/20 +…+ 1/132 = 1/(1.2) + 1/(2.3) + 1/(3.4) + 1/(4.5) +…+1/(11.12)
= (1 – 1/2) + (1/2 – 1/3) + (1/3 – 1/4) + (1/4 – 1/5) +…+ (1/11 – 1/12)
= 1 – 1/12 = 11/12
Vậy x = (15/16) : (11/12) = 45/44.
29 tháng 4 2015
(1/2+1/4+1/8+1/16):x=1/2+1/6+1/12+1/20+...+1/132
(1-1/2+1/2-1/4+1/4-1/8+1/8-1/16):x=1/1x2+1/2x3+1/3x4+1/4x5+...+1/11x12
(1-1/16):x=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/11-1/12
15/16:x=1-1/12
15/16:x=11/12
x=15/16:11/12
x=45/44
LI
1
HV
12 tháng 3 2016
(1/2+1/4+1/8+1/16):x=1/2+1/6+1/12+.....+1/132
15/16 : x = 1/1x2+1/2x3+1/3x4+.........+1/11x12
15/16 : x = 1-1/2+1/2-1/3+1/3-1/4+........+1/11-1/12
15/16 :x = 1-1/12
15/16 : x = 11/12
x = 15/16 : 11/12
x= 45/44
TK
1
3 tháng 7 2021
Giải:
a) \(\dfrac{-5}{8}=\dfrac{x}{16}\)
\(\Rightarrow x=\dfrac{16.-5}{8}=-10\)
\(\dfrac{3x}{9}=\dfrac{2}{6}\)
\(\Rightarrow3x=\dfrac{2.9}{6}=3\)
\(\Rightarrow x=1\)
b) \(\dfrac{x+3}{15}=\dfrac{1}{3}\)
\(\Rightarrow x+3=\dfrac{1.15}{3}=5\)
\(\Rightarrow x=2\)
\(\dfrac{6}{2x+1}=\dfrac{2}{7}\)
\(\Rightarrow2x+1=\dfrac{6.7}{2}=21\)
\(\Rightarrow x=10\)
c) \(\dfrac{4}{x-6}=\dfrac{y}{24}=\dfrac{-12}{18}\)
\(\Rightarrow\dfrac{4}{x-6}=\dfrac{-12}{18}\)
\(\Rightarrow x-6=\dfrac{18.4}{-12}=-6\)
\(\Rightarrow x=0\)
\(\Rightarrow\dfrac{y}{24}=\dfrac{-12}{18}\)
\(\Rightarrow y=\dfrac{-12.24}{18}=-16\)
\(\dfrac{3-x}{-12}=\dfrac{16}{y+1}=\dfrac{192}{-72}\)
\(\Rightarrow\dfrac{3-x}{-12}=\dfrac{192}{-72}\)
\(\Rightarrow3-x=\dfrac{192.-12}{-72}=32\)
\(\Rightarrow x=-29\)
\(\Rightarrow\dfrac{16}{y+1}=\dfrac{192}{-72}\)
\(\Rightarrow y+1=\dfrac{16.-72}{192}=-6\)
d) \(\dfrac{-2}{3}< \dfrac{x}{5}< \dfrac{-1}{6}\)
\(\Rightarrow\dfrac{-20}{30}< \dfrac{6x}{30}< \dfrac{-5}{30}\)
\(\Rightarrow6x\in\left\{-18;-12;-6\right\}\)
\(\Rightarrow x\in\left\{-3;-2;-1\right\}\)
\(\dfrac{-1}{5}\le\dfrac{x}{8}\le\dfrac{1}{4}\)
\(\Rightarrow\dfrac{-8}{40}\le\dfrac{5x}{40}\le\dfrac{10}{40}\)
\(\Rightarrow5x\in\left\{-5;0;5;10\right\}\)
\(\Rightarrow x\in\left\{-1;0;1;2\right\}\)
e) \(\dfrac{x+46}{20}=x\dfrac{2}{5}\)
\(\Rightarrow\dfrac{x+46}{20}=x+\dfrac{2}{5}\)
\(\Rightarrow\dfrac{x+46}{20}=\dfrac{5x+2}{5}\)
\(\Rightarrow5.\left(x+46\right)=20.\left(5x+2\right)\)
\(\Rightarrow5x+230=100x+40\)
\(\Rightarrow5x-100x=40-230\)
\(\Rightarrow-95x=-190\)
\(\Rightarrow x=-190:-95\)
\(\Rightarrow x=2\)
\(y\dfrac{5}{y}=\dfrac{86}{y}\)
\(\Rightarrow y+\dfrac{5}{y}=\dfrac{86}{y}\)
\(\Rightarrow\dfrac{y^2+5}{y}=\dfrac{86}{y}\)
\(\Rightarrow y^2+5=86\)
\(\Rightarrow y^2=86-5\)
\(\Rightarrow y^2=81\)
\(\Rightarrow\left[{}\begin{matrix}y=9\\y=-9\end{matrix}\right.\)
Chúc bạn học tốt!
30 tháng 5 2015
\(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right):x=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}\)
\(\Rightarrow\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}\right):x=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}\)
\(\Rightarrow\left(1-\frac{1}{16}\right):x=1-\frac{1}{5}\)
\(\Rightarrow\frac{15}{16}:x=\frac{4}{5}\)
\(\Rightarrow x=\frac{15}{16}:\frac{4}{5}=1\frac{11}{64}\)
NL
15 tháng 4 2019
2n+1/n+1 có gt nguyên
<=>2n+2-1/n+1
2(n+1)-1/n+1
2-(1/n+1)
để 2n+1/n+1 có gt nguyên
<=>1/n+1 có gt nguyên
=>n+1 thuộc {+_1}
lm tiếp nhé
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