2012/1.2+2012/2.3+...+2012/2011.2012 = ?
Những câu hỏi liên quan
tinh : (1.2 +2.3+3.4+...+2010.2011.2011+2012) +( 1+2+3+...+2011+2012) =
Cho \(S=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2011.2012}\)
Xem chi tiết
Tính A = 2012.S
S = 1/2 - 1/3 + 1/3 -1/4 + ......... +1/2011 -1/2012
S= 1/2 - 1/2012 = 1005/2012
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\(S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...-\frac{1}{2012}\)
\(S=\frac{1}{2}+0+0+0+...-\frac{1}{2012}\)
\(S=\frac{1}{2}-\frac{1}{2012}\)
\(S=\frac{1005}{2012}\)
\(A=\frac{2012}{1}\cdot\frac{1005}{2012}\)
\(A=1005\)
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\(\Leftrightarrow S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...+\frac{1}{2011}-\frac{1}{2012}\)
\(\Rightarrow S=\frac{1}{2}-\frac{1}{2012}=\frac{1005}{2012}\)
=>A=\(\frac{2012\cdot1005}{1\cdot2012}=\frac{1005}{1}=1005\)
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($\frac{1}{1.2}$ + $\frac{1}{2.3}$ + $\frac{1}{3.4}$ + ... + $\frac{1}{2011. 2012}$ ) x = 2011
\(\Leftrightarrow x\cdot\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2011}-\dfrac{1}{2012}\right)=2011\)
\(\Leftrightarrow x\cdot\dfrac{2011}{2012}=2011\)
hay x=2012
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\(\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{2011.2012}\right)x=2011\)
\(\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2011}-\dfrac{1}{2012}\right)x=2011\)
\(\left(\dfrac{1}{1}-\dfrac{1}{2012}\right)x=2011\)
\(\dfrac{2011}{2012}x=2011\)
\(x=2012\)
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`(1/[1.2]+1/[2.3]+1/[3.4]+....+1/[2011.2012])x=2011`
`(1-1/2+1/2-1/3+1/3-1/4+.....+1/2011-1/2012)x=2011`
`(1-1/2012)x=2011`
`2011/2012x=2011`
`x=2011:2011/2012`
`x=2012`
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Xem thêm câu trả lời
Chứng minh rằng:
A=1/1.2+1/3.4+...+1/2011.2012=1/2007+1/2008+...+1/2012
Ai giúp mình vs nhé mình đang cần gấp.Thanks bạn nào giúp mình!
Giải Pt :
a) \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+........+\frac{1}{x\left(x+1\right)}=\frac{\sqrt{2012-x}+2012}{\sqrt{2012-x}+2013}\)
b) \(\sqrt{2x+3}+\sqrt{x+1}=3x+2\sqrt{2x^2+5x+3}-16\)
b) \(\left(\sqrt{2x+3}-3\right)+\left(\sqrt{x+1}-2\right)+5=3x+2\left(\sqrt{2x^2+5x+3}-6\right)+12-16\)
\(\Leftrightarrow\left(\sqrt{2x+3}-3\right)+\left(\sqrt{x+1}-2\right)=3\left(x-3\right)+2\left(\sqrt{2x^2+5x+3}-6\right)\)
\(\Leftrightarrow\frac{2\left(x-3\right)}{\sqrt{2x+3}+3}+\frac{x-3}{\sqrt{x+1}+2}-3\left(x-3\right)-\frac{2\left(x-3\right)\left(2x+11\right)}{\sqrt{2x^2+5x+3}+6}=0\Leftrightarrow x-3=0\Leftrightarrow x=3.\)
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Câu 1:So sánh M= 1/1.2+1/2.3+...+1/49.50 với 1
Câu 2: Tính. B=1+2+2^2+2^3+...+2^2008/1-2^2009
Câu 3.Tính. B=1/2+1/6+1/12+1/20+1/30+...+1/9900
Câu 4.Tính. 1/1.3+1/3.5+1/5.7+...+1/2009.2011
Câu 5. So sánh:
A=2011+2012/2012+2013
Và B=2011/2012+2011/2012+2012/2013
Câu 6: Tìm x biết :.(x/7+0,25)=-1/28
So sánh A với B:
a:A=-2012/4025;B=-1999/3997
b:A=2011/1.2+2011/3.4+.....+2011/1999.2000; B=2012/1001+2012+1002+...+2012/2000
$A=\frac{2011}{1.2}+\frac{2011}{3.4}+\frac{2011}{5.6}+...+\frac{2011}{1999.2000}$
$B=\frac{2012}{1001}+\frac{2012}{1002}+\frac{2012}{1003}+...\frac{2012}{2000}$
Giải phương trình: \(\left(\dfrac{1}{1.2}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\right)2013x=\dfrac{2012}{51}+\dfrac{2012}{52}+\dfrac{2012}{99}+\dfrac{2012}{100}\)
\(\frac{1}{1.2}+\frac{1}{3.4}+....+\frac{1}{99.100}=\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{99}-\frac{1}{100}\)
\(=\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+....+\frac{1}{100}-2.\left(\frac{1}{2}+\frac{1}{4}+.....+\frac{1}{100}\right)\)
\(=\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+....+\frac{1}{100}-1-\frac{1}{2}-\frac{1}{3}-....-\frac{1}{50}=\frac{1}{51}+\frac{1}{52}+...+\frac{1}{100}\)
=> \(2013x.\left(\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)=2013x.\left(\frac{1}{51}+\frac{1}{52}+...+\frac{1}{100}\right)\)
=> \(2013x.\left(\frac{1}{51}+\frac{1}{52}+...+\frac{1}{100}\right)=2012.\left(\frac{1}{51}+\frac{1}{52}+...+\frac{1}{100}\right)\Rightarrow2013x=2012\Rightarrow x=\frac{2012}{2013}\)
Vậy \(x=\frac{2012}{2013}\)
p/s: --trình bày sai sót mong bỏ qua
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