1. so sanh a với b biet
\(a=\frac{1x2}{2x2}x\frac{2x3}{3x3}x\frac{3x4}{4x4}x\frac{4x5}{5x5}x....x\frac{2012x2013}{2013x2013}\)
\(b=\frac{2012x2013-2012x2012}{2012x2011+2012x2}\)
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1.so sanh a voi b biet
\(a=\frac{1x2}{2x2}x\frac{2x3}{3x3}x\frac{3x4}{4x4}x\frac{4x5}{5x5}x.....x\frac{2012x2013}{2013x2013}\)
\(b=\frac{2012x2013-2012x2012}{2012x2011+2012x2}\)
AI LÀM DUNG NHAT ,DAU TIEN MINH LIKE
so sánh A và B:
A=1x2/2x2 x 2x3/3x3 x 3x4/4x4 x 4x5/5x5 x...x2019x2020/2020x2020
B=2020x2021-2021x2019/2021x2017+2021x3
Tính
A=1x2x3+2x3x3+3x4x3+4x5x3+....+98x99x3
B=1x2+2x3+3x4+4x5+...+98x99
C=1x1+2x2+3x3+4x4+5x5+...+98x98
A=1.2.3+2.3(4-1)+3.4(5-2)+4.5(6-3)+....+98.99(100-97) "." la dau nhan
A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+4.5.6-3.4.5+....+98.99.100-97.98.99
A=1.2.3+98.99.100
A= 970206
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Ta có : B = 1.2 + 2.3 + 3.4 + ..... + 98.99
=> 3B = 0.1.2 + 1.2.3 - 1.2.3 + ...... + 98.99.100
=> 3B = 98.99.100
=> B = \(\frac{98.99.100}{3}\) = 323400
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C = 1.1 + 2.2 + 3.3 + ..... + 98.98
=> C = 1.(2 - 1) + 2(3 - 1) + 3(4 - 1) + ...... + 98(99 - 1)
=> C = 1.2 - 1 + 2.3 - 2 + 3.4 - 3 + ..... + 98.99 - 98
=> C = (1.2 + 2.3 + 3.4 + ..... + 98.99) - (1 + 2 + 3 + ..... + 98)
=> C = 323400 - 4851
=> C = 318549.
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Chứng tỏ rằng
B=\(\frac{1}{2x2}+\frac{1}{3x3}+\frac{1}{4x4}+\frac{1}{5x5}+\frac{1}{6x6}+\frac{1}{7x7}+\frac{1}{8x8}< 1\)
Ta thấy:
1/2*2<1/1*2)vì 2*2>1*2).
1/3*3<1/2*3(vì 3*3>2*3).
...
1/8*8<1/7*8(vì 8*8>7*8).
=>1/2*2+1/3*3+1/4*4+...+1/8*8<1/1*2+1/2*3+1/3*4+...+1/7*8.
=>B<1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8.
=>B<1-1/8.
=>B<7/8.
Mà 7/8<1.
=>B<1.
Vậy B<1(đpcm).
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\(< \frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}\)
\(\Rightarrow1-\frac{1}{8}< 1\)
=>B<1
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\(B=\frac{1}{2.2}+\frac{1}{3.3}+\frac{1}{4.4}+\frac{1}{5.5}+\frac{1}{6.6.}+\frac{1}{7.7}+\frac{1}{8.8}\)\(=\)\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+\frac{1}{8^2}\)
\(B=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)
\(B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{7}-\frac{1}{8}\)
\(B=1-\frac{1}{8}\)
\(\Rightarrow B< 1\left(ĐPCM\right)\)
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Tìm y biết:
a) (y+2):5-5x5=378
b) (7,56x0,99+7,56x0,01)x(y+2)=18,9
c) (y+\(\frac{1}{1x2}\))+(y+\(\frac{1}{2x3}\))+(y+\(\frac{1}{3x4}\))+...+(y+\(\frac{1}{2013x2014}\))=\(\frac{2013}{2014}\)
a)(y+2):5-5x5=378
(y+2):5-25=378
(y+2):5=378+25
(y+2):5=403
(y+2)=403x5
y+2=2015
y=2015-2
y=2013
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(y+2):5-5.5=378
(y+2):5-25=378
(y+20)=378+25
(y+2)=403
(y+2)=403.5
y+2=2015
y=2015-2
y=2013
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a) \(\left(y+2\right):5-5.5=378\)
\(\left(y+2\right):5-25=378\)
\(\left(y+2\right):5=378+25\)
\(\left(y+2\right):5=403\)
\(y+2=403.5\)
\(y+2=2015\)
\(y=2015-2\)
\(y=2013\)
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\(\frac{1}{2x3}x\frac{1}{3x4}x\frac{1}{4x5}x............x\frac{1}{98x99}x\frac{1}{99x100}\)
Hãy tính nhanh ,ai nhanh mình tick cho
\(=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}\)
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\(\Leftrightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(\Rightarrow\frac{1}{2}-0+0+...+0-\frac{1}{100}\)
\(\Rightarrow\frac{50}{100}-\frac{1}{100}=\frac{49}{100}\)
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\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+..............+\frac{1}{8x9}=?\)
\(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+...+\frac{1}{8x9}\)
=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}\)
=\(1-\frac{1}{9}\)
=\(\frac{8}{9}\)
OK XONG NHỚ CHO MIK NHA
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\(\frac{1}{1\times2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+.......+\frac{1}{7x8}+\)\(\frac{1}{8x9}\)
=1-\(\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{8}-\frac{1}{9}\)
=1-\(\frac{1}{9}\)
=\(\frac{8}{9}\)
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\(\frac{1}{1\times2}+........+\frac{1}{8\times9}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+......+\frac{1}{9}-\frac{1}{10}\)
\(=1-\frac{1}{10}=\frac{9}{10}\)
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\(\)Tính
\(\frac{1}{1x2}x\frac{4}{2x3}x\frac{9}{3x4}x.......x\frac{10000}{100x101}\)
\(\frac{1}{1x2}x\frac{4}{2x3}x\frac{9}{3x4}x...x\frac{10000}{100x101}=\frac{1x1}{1x2}x\frac{2x2}{2x3}x\frac{3x3}{3x4}x...x\frac{100x100}{100x101}\)
=\(\frac{1x2x3x...x100}{1x2x3x...x100}x\frac{1x2x3x...x100}{2x3x4x...x101}=1x\frac{1}{101}=\frac{1}{101}\)
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Tính nhanh
A = \(\frac{3}{1x2}+\frac{7}{3x4}+\frac{11}{5x6}+\frac{15}{7x8}\) và B = \(\frac{5}{2x3}+\frac{9}{4x5}+\frac{13}{6x7}\)