A=(1/2+1).(1/3+1).(1/4+1)...(1/2011+1)
Những câu hỏi liên quan
So sanh A voi 1:
A=1/2*2 + 1/3*3 + 1/4*4 + .....+1/2011*2011
So sanh B voi 3/4:
B=1/2*2 + 1/3*3 +1/4*4 + ......+1/2011*2011
ai đó giúp mk với mk xin chân thành cảm ơn! a=(2010+2010/2+2009/3+2008/4+...+1/2011/ 1/2+1/3+...+1/2011) / (1/2+1/3+1/4+1/5+...+1/2009+1/2010+1/2011)
1) Tìm x, y, z biết rằng x^2+y^2+z^2=xy+yz+xz và x^2011+y^2011+z^2011=3^2012
2) Tính A= (1^4+1/4)(3^4+1/4)(5^4+1/4)....(2011^4+1/4) / (2^4+1/4)(4^4+1/4)(6^4+1/4)....(2012^4+1/4)
x2+y2+z2= xy+yz+zx.
=> 2x2+2y2+2z2-2xy-2yz-2zx=0
=> ( x-y)2+(y-z.)2+(z-x)2 =0
=> x=y=z=0
Thay x=y=z vào x2011+y2011+z2011=32012 ta được:
3.x2011=3.32011
=> x2011=32011
=> x=3 hoặc x = -3
Hay x=y=z=3 hoặc x=y=z=-3
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1) có bn giải rồi ko giải nữa
2) \(A=\frac{\left(1^4+\frac{1}{4}\right)\left(3^4+\frac{1}{4}\right)\left(5^4+\frac{1}{4}\right)....\left(2011^4+\frac{1}{4}\right)}{\left(2^4+\frac{1}{4}\right)\left(4^4+\frac{1}{4}\right)\left(6^4+\frac{1}{4}\right)....\left(2012^4+\frac{1}{4}\right)}\)
Với mọi n thuộc N ta có :
\(n^4+\frac{1}{4}=\left(n^4+2.\frac{1}{2}.n^2+\frac{1}{4}\right)-n^2=\left(n^2+\frac{1}{2}\right)^2-n^2=\left(n^2-n+\frac{1}{2}\right)\left(n^2+n+\frac{1}{2}\right)\)
\(=\left[n\left(n-1\right)+\frac{1}{2}\right]\left[n\left(n+1\right)+\frac{1}{2}\right]\)
Áp dụng ta được :
\(A=\frac{\frac{1}{2}\left(1.2+\frac{1}{2}\right)\left(2.3+\frac{1}{2}\right)\left(3.4+\frac{1}{2}\right)....\left(2011.2012+\frac{1}{2}\right)}{\left(1.2+\frac{1}{2}\right)\left(2.3+\frac{1}{2}\right)\left(3.4+\frac{1}{2}\right).......\left(2012.2013+\frac{1}{2}\right)}\)
\(=\frac{\frac{1}{2}}{2012.2013+\frac{1}{2}}=\frac{1}{8100313}\)
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Cho A=1/2+1/3+1/4+...+1/2011+1/2012
B=2011/1+2010/2+2009/3+...+2/2010+1/2011
Tính A/B
Ta có \(B=\left(\frac{2010}{2}+1\right)+\left(\frac{2009}{3}+1\right)+...+\left(\frac{2}{2010}+1\right)+\left(\frac{1}{2011}+1\right)+1\)
\(B=\frac{2012}{2}+\frac{2012}{3}+...+\frac{2012}{2010}+\frac{2012}{2011}+\frac{2012}{2012}\)
\(B=2012.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2010}+\frac{1}{2011}+\frac{1}{2012}\right)\)
B=2012.A
=>A/B=1/2012
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Xem thêm câu trả lời
1. Cho A= 1/2 + 1/3 + 1/4 + ... + 1/2011 + 1/ 2012 và B= 2011/1 + 2010/2 + 2009/3 + ...+ 2/2010 + 1/2011
Tính: B/A { Giúp mik nhé ths }
Cho A=1/2*2+1/3*3+1/4*4+...+1/2011*2011
a)So Sánh A với 1
B)so sánh A với 3/4
Tính S=\(\frac{1}{1^4+1^2+1}+\frac{2}{2^4+2^2+1}+\frac{3}{3^4+3^2+1}+......+\frac{2011}{2011^4+2011^2+1}\)
Ta có: \(2.S=2.\left(\frac{1}{1^4+1^2+1}+...+\frac{2011}{2011^4+2011^2+1}\right)\)
Xét hạng tử tống quát: \(\frac{2.n}{n^4+n^2+1}=\frac{2.n}{\left(n^4+2n^2+1\right)-n^2}=\frac{\left(n^2+n+1\right)-\left(n^2-n+1\right)}{\left(n^2-n+1\right)\left(n^2+n+1\right)}\)\(=\frac{1}{n^2-n+1}-\frac{1}{n^2+n+1}\)
Từ đó: \(\frac{2.1}{1^4+1^2+1}=\frac{1}{1}-\frac{1}{3}\)
\(\frac{2.2}{2^4+2^2+1}=\frac{1}{3}-\frac{1}{7}\)
.....
\(\frac{2.2011}{2011^4+2011^2+1}=\frac{1}{4042111}-\frac{1}{4046133}\)
Từ đó => 2.S= \(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{7}+...+\frac{1}{4042111}-\frac{1}{4046133}\)=\(1-\frac{1}{4046133}\)=\(\frac{4046132}{4046133}\)
=> S\(=\frac{2023066}{4046133}\)
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in1. So sánh A và B, biết:A20112011+2/20112011-1B20112011/20112011-32.tính(217+417)(314-312)(24-42)/152+533.chứng tỏ rằng:1/22+1/32+1/42+...+1/2010214. Tính a2, biết:a 2.9.8+3.12.10+4.15.12+...+98.297.200/2.3.4+3.4.5+4.5.6+...+98.99.100
Đọc tiếp
in1. So sánh A và B, biết:
A=20112011+2/20112011-1
B=20112011/20112011-3
2.tính
(217+417)(314-312)(24-42)/152+53
3.chứng tỏ rằng:
1/22+1/32+1/42+...+1/20102<1
4. Tính a2, biết:
a= 2.9.8+3.12.10+4.15.12+...+98.297.200/2.3.4+3.4.5+4.5.6+...+98.99.100
Bài 3:
Ta có:
\(\frac{1}{2^2}\)+\(\frac{1}{3^2}\)+\(...\)+\(\frac{1}{2010^2}\)<\(\frac{1}{1.2}\)+\(\frac{1}{2.3}\)+...+\(\frac{1}{2009.2010}\)
Xét:\(\frac{1}{1.2}\)+\(\frac{1}{2.3}\)+.....+\(\frac{1}{2009+2010}\)=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2009}-\frac{1}{2010}\)=\(1-\frac{1}{2010}\)<1
\(\Rightarrow\)\(\frac{1}{2^2}+\frac{1}{3^2}+....+\frac{1}{2010^2}< 1\)
\(\)Vậy \(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{2010^2}< 1\)
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1. Tìm x
x + 2011+ x+ 2008/2 + x + 2007/3+ x + 2008/4 + x + 2011/5 =-15
2.
Cho A = (1/2^2-1) × (1/3^2 -1) ×(1/4^2 -1) ×...(1/400^2 -1). So sánh A với -1/2
Tìm x:
x . (1/2+1/3+1/4+. . .+1/2011+1/2012)
2012/1+2011/2+2010/3+2009/4+ . . . +2/2011+1/2012
=1