tìm x
1/2013 *x+1+1/2+1/6+1/12+...+1/2012.2013=2
NH
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Tìm x biết : 1/2013.x +1+1/2+1/6+1/12+...+1/2012.2013=2
1/2013.x+1+1/2+1/6+1/12+...+1/2012.2013=2
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Tìm x
\(\frac{1}{2013}x+1+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{2012.2013}=2\)
\(\frac{1}{2013}x+1+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{2012.2013}=2\)
\(\frac{1}{2013}x+1+(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2012.2013})=2\)
\(\frac{1}{2013}x+1+\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2012}-\frac{1}{2013}\right)=2\)
\(\frac{1}{2013}x+1+\left(1-\frac{1}{2013}\right)=2\)
\(\frac{1}{2013}x+1+1-\frac{1}{2013}=2\)
\(\frac{1}{2013}x-\frac{1}{2013}+2=2\)
\(\frac{1}{2013}.\left(x-1\right)=2-2\)
\(\frac{1}{2013}.\left(x-1\right)=0\)
=> x - 1 = 0
x = 1
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\(\frac{1}{2013}x+1+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{2012.2013}=2\)
\(\frac{1}{2013}x+\left(1+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2012.2013}\right)=2\)
\(\frac{1}{2013}x+\left(1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2012}-\frac{1}{2013}\right)=2\)
\(\frac{1}{2013}x+\left(1-\frac{1}{2013}\right)=2\)
\(\frac{1}{2013}x+\frac{2012}{2013}=2\)
\(\frac{1}{2013}x=2-\frac{2012}{2013}\)
\(\frac{1}{2013}x=\frac{2014}{2013}\)
\(x=\frac{2014}{2013}:\frac{1}{2013}\)
=> x=2014
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tìm x thuộc N biết 1/2013.x+1+1/2+1/6+....+1/2012.2013=2
\(\frac{1}{2013}.x+1+\frac{1}{2}+\frac{1}{6}+...+\frac{1}{2012.2013}=2\)
\(\Rightarrow\frac{1}{2013}.x+1+\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2012.2013}=2\)
\(\Rightarrow\frac{1}{2013}.x+1+\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2012}-\frac{1}{2013}=2\)
\(\Rightarrow\frac{1}{2013}.x+1+\frac{1}{1}-\frac{1}{2013}=2\)
\(\Rightarrow\frac{1}{2013}.x+2-\frac{1}{2013}=2\)
\(\Rightarrow\frac{1}{2013}.x=\frac{1}{2013}\Rightarrow x=1\)
Vậy x=1
CHÚC CÁC EM HỌC TỐT
1/5.8+1/8.11+....+1/y(y+3)=98/1545 tìm x,y
2x+7/6+13/12+21/20+31/30+43/42+57/56+73/72+91/90=10
1/2013.x+1+1/2+1/6+....+1/2012.2013=2
1+1/3+1/6+1/10+...+1/2012.2013=2
1/21+1/28+1/36+...+2/x(x+1)=2/9
ai nhanh mình tik cho
1 .Tìm x biết
a. ( dfrac{1}{1.4}+dfrac{1}{4.7}+dfrac{1}{7.10}+...+dfrac{1}{97.100}) dfrac{0,33x}{2009}
b. 1 + dfrac{1}{3}+dfrac{1}{6}+dfrac{1}{10}+...+dfrac{2}{xleft(x+1right)}1dfrac{1991}{1993}
c. dfrac{1}{2013}x+1+dfrac{1}{2}+dfrac{1}{6}+dfrac{1}{12}+...+dfrac{1}{2012.2013}2
d. 2x + dfrac{7}{6}+dfrac{13}{12}+dfrac{21}{20}+dfrac{31}{30}+dfrac{43}{42}+dfrac{57}{56}+dfrac{73}{72}+dfrac{91}{90}10
2. Chứng minh rằng :
a. dfrac{1}{4}+dfrac{1}{4^2}+dfrac{1}{4^3}+...+dfrac{1}{4^{99}} dfrac{1}{3...
Đọc tiếp
1 .Tìm x biết
a. ( \(\dfrac{1}{1.4}+\dfrac{1}{4.7}+\dfrac{1}{7.10}+...+\dfrac{1}{97.100}\)) = \(\dfrac{0,33x}{2009}\)
b. 1 + \(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+...+\dfrac{2}{x\left(x+1\right)}=1\dfrac{1991}{1993}\)
c. \(\dfrac{1}{2013}x+1+\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{2012.2013}=2\)
d. 2x + \(\dfrac{7}{6}+\dfrac{13}{12}+\dfrac{21}{20}+\dfrac{31}{30}+\dfrac{43}{42}+\dfrac{57}{56}+\dfrac{73}{72}+\dfrac{91}{90}=10\)
2. Chứng minh rằng :
a. \(\dfrac{1}{4}+\dfrac{1}{4^2}+\dfrac{1}{4^3}+...+\dfrac{1}{4^{99}}< \dfrac{1}{3}\)
b. \(\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+...+\dfrac{1}{18.19.20}< \dfrac{1}{4}\)
1/
a) ta có \(\dfrac{1}{1.4}+\dfrac{1}{4.7}+...+\dfrac{1}{97.100}=\dfrac{1}{3}.\left(\dfrac{3}{1.4}+\dfrac{3}{4.7}+...+\dfrac{3}{97.100}\right)\)
\(=\dfrac{1}{3}.\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{97}-\dfrac{1}{100}\right)\)
\(=\dfrac{1}{3}.\dfrac{99}{100}=\dfrac{33}{100}\)
⇒ \(\dfrac{33}{100}=\dfrac{0,33x}{2009}\)
⇒ \(\dfrac{33}{100}=\dfrac{0,33}{2009}.x\Rightarrow x=\dfrac{33}{100}:\dfrac{0,33}{2009}=2009\)
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b,1 + 1/3 + 1/6 + 1/10 + ... + 2/x(x+1)=1 1991/1993
2 + 2/6 + 2/12 + 2/20 + ... + 2/x(x+1) = 3984/1993
2.(1/1.2 + 1/2.3 + 1/3.4 + ... + 1/x(x+1) = 3984/1993
2.(1 − 1/2 + 1/2 − 1/3 + ... + 1/x − 1/x+1)=3984/1993
2.(1 − 1/x+1) = 3984/1993
1 − 1/x + 1= 3984/1993 :2
1 − 1/x+1 = 1992/1993
1/x+1 = 1 − 1992/1993
1/x+1=1/1993
<=>x+1 = 1993
<=>x+1=1993
<=> x+1=1993
<=> x = 1993-1
<=> x = 1992
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Bài 1:
c: \(\Leftrightarrow x\cdot\dfrac{1}{2013}+1+1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2012}-\dfrac{1}{2013}=2\)
\(\Leftrightarrow x\cdot\dfrac{1}{2013}+2-\dfrac{1}{2013}=2\)
=>x*1/2013=1/2013
=>x=1
d: \(\Leftrightarrow2x+8+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{90}=10\)
=>2x+1/2-1/3+1/3-1/4+...+1/9-1/10=2
=>2x+2/5=2
=>x+1/5=1
=>x=4/5
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So sánh:
A= 2010/2011 - 2011/2012 + 2012/2013 - 2013/ 2014 và B= 1/ 2010.2011 - 1/ 2012.2013
\(A=\left(1-\frac{1}{2011}\right)-\left(1-\frac{1}{2012}\right)+\left(1-\frac{1}{2013}\right)-\left(1-\frac{1}{2014}\right)\)
\(=1-\frac{1}{2011}-1+\frac{1}{2012}+1-\frac{1}{2013}-1+\frac{1}{2014}\)
\(=\left(1-1+1-1\right)-\left(\frac{1}{2011}+\frac{1}{2012}-\frac{1}{2013}+\frac{1}{2014}\right)\)
còn lại bó tay @@
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\(A=\frac{2010}{2011}-\frac{2011}{2012}+\frac{2012}{2013}-\frac{2013}{2014}\)
và
\(B=\frac{1}{2010.2011}-\frac{1}{2012.2013}\)
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bài 1:tìm số tự nhiên n sao cho 6n+3 chia hết cho 3n+6
bài 2:a,tìm số hữu tỷ có dạng 7/a biết số đó>-9/11 và nhỏ hơn -9/13
b,so sánh A=2012/2013-2013/2014+2014/2015-2015/2016 và B=-1/2012.2013 -1/2014.2015
c,cho số tự nhiên a.người ta đổi chỗ các chữ số của A để dc B gấp 3 lần A.CMR:b chia hết cho 27
nhanh lên nha các bn mk cần gấp lắm
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1/2 +1/6+1/12+....+1/x.(x+1)=2013/2014 giúp mình nha!
Ta goi day tren la A.Ta co:A=1/2+1/6+1/12+1/20+...+1/x(x+1)=2013/2014
A=1/(1*2)+1/(2*3)+1/(3*4)+...+1/x(x+1)=2013/2014
A=1-1/2+1/2-1/3+1/3-1/4+...+1/x-1/x+1.=2013/2014
A=1-1/x+1=2013/2014
Suy ra:1/x+1=1-2013/2014
1/1+1=1/2014
Suy ra x+1=2014
Suy ra x=2013
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