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PT
3
13 tháng 8 2015
\(2x+1+\frac{1}{6}+1+\frac{1}{12}+..+1+\frac{1}{90}=10\)
=> 2x + 8 + \(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}=10\)
=> 2x + \(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}=10-8\)
\(2x+1-\frac{1}{10}=2\)
=> 2x + \(\frac{9}{10}=2\)
=> 2x = 2 - 9/10
=>2x = 11/10
=> x = 11/10 : 2
x = 11/20
SN
1
NL
Nguyễn Lê Phước Thịnh
CTVHS
23 tháng 5 2022
\(=1+1+1+1+1+1+1+1+1+\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\right)\)
\(=9+\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\)
=9+9/10=99/10
NL
Nguyễn Lê Phước Thịnh
CTVHS
28 tháng 5 2022
a: \(\dfrac{2032-x}{25}+\dfrac{2053-x}{23}+\dfrac{2070-x}{21}+\dfrac{2083-x}{19}-10=0\)
\(\Leftrightarrow\left(\dfrac{2032-x}{25}-1\right)+\left(\dfrac{2053-x}{23}-2\right)+\left(\dfrac{2070-x}{21}-3\right)+\left(\dfrac{2083-x}{19}-4\right)=0\)
=>2007-x=0
hay x=2007
b: \(\Leftrightarrow x+\left(1+1+1+1+1+1+1\right)+\left(\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\right)=0\)
\(\Leftrightarrow x+7+\left(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)=0\)
=>x+7+1/3-1/10=0
hay x=-217/30
TT
11 tháng 11 2017
\(\dfrac{3}{2}+\dfrac{13}{6}+\dfrac{37}{12}+\dfrac{81}{20}+\dfrac{151}{30}+\dfrac{253}{42}+\dfrac{393}{56}+\dfrac{577}{72}+\dfrac{811}{90}\)
\(=\dfrac{459}{10}\)
QH
11 tháng 11 2017
\(\dfrac{3}{2}+\dfrac{13}{6}+\dfrac{37}{12}+\dfrac{81}{20}+\dfrac{151}{30}+\dfrac{253}{42}+\dfrac{393}{56}+\dfrac{577}{72}+\dfrac{811}{90}\)\(=\dfrac{2}{2}+\dfrac{1}{2}+\dfrac{12}{6}+\dfrac{1}{6}+\dfrac{36}{12}+\dfrac{1}{12}+\dfrac{80}{20}+\dfrac{1}{20}+\dfrac{150}{30}+\dfrac{1}{30}+\dfrac{252}{42}+\dfrac{1}{42}+\dfrac{392}{56}+\dfrac{1}{56}+\dfrac{576}{72}+\dfrac{1}{72}+\dfrac{810}{90}+\dfrac{1}{90}\)\(=1+\dfrac{1}{2}+2+\dfrac{1}{6}+3+\dfrac{1}{12}+4+\dfrac{1}{20}+5+\dfrac{1}{30}+6+\dfrac{1}{42}+7+\dfrac{1}{56}+8+\dfrac{1}{72}+9+\dfrac{1}{90}\)\(=\left(1+2+3+4+5+6+7+8+9\right)+\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\right)\)= 45 + \(\dfrac{9}{10}\)
= \(\dfrac{459}{10}\)
Ta có: \(2x+\frac76+\frac{13}{12}+\frac{21}{20}+\frac{31}{30}+\frac{43}{42}+\frac{57}{56}+\frac{73}{72}+\frac{91}{90}=10\)
=>\(2x+1+\frac16+1+\frac{1}{12}+\ldots+1+\frac{1}{90}=10\)
=>\(2x+8+\left(\frac16+\frac{1}{12}+\cdots+\frac{1}{90}\right)=10\)
=>\(2x+8+\left(\frac12-\frac13+\frac13-\frac14+\cdots+\frac19-\frac{1}{10}\right)=10\)
=>\(2x+8+\left(\frac12-\frac{1}{10}\right)=10\)
=>\(2x+8+\frac{4}{10}=10\)
=>\(2x=10-8-\frac{4}{10}=2-\frac{4}{10}=2-\frac25=\frac85\)
=>\(x=\frac85:2=\frac45\)