so sánh : 12/1x3 +22/3x5 +. . .+ 10082/2015x2017 với 504
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so sánh : 12/1x3 +22/3x5 +. . .+ 10082/2015x2017 với 504
1/2x(1+1/1x3)x(1+1/2x4)x(1+1/3x5)x........x(1+1/2015x2017)
ai help tui với🥹🥹🥹🥹
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1/2x(1+1/1x3)x(1+1/2x4)x(1+1/3x5)x........x(1+1/2015x2017)
ai help tui với🥹🥹🥹🥹
Bạn xem bài tương tự tại đây. Đề là:
Tính $(1+\frac{1}{1.3})(1+\frac{1}{2.4})....(1+\frac{1}{2021.2023})$
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chứng minh rằng tổng S=1/1x3+1/3x5+1/5x7+.............+1/2015x2017<1/2
\(S=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2015.2017}\)
\(S=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2015}-\frac{1}{2017}\right)\)
\(S=\frac{1}{2}.\left(1-\frac{1}{2017}\right)\)
\(S=\frac{1}{2}.\frac{2016}{2017}\)
\(S=\frac{1008}{2017}< \frac{1}{2}\)
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\(S=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2015.2017}\)
\(2S=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2015.2017}\)
\(2S=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2015}-\frac{1}{2017}\)
\(2S=1-\frac{1}{2017}< 1\)
=> 2S < 1
=> S < \(\frac{1}{2}\)(đpcm)
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S = \(\frac{1}{2}\). \(\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{2015.2017}\right)\)
= \(\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2015}-\frac{1}{2017}\right)\)
= \(\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{2017}\right)\)= \(\frac{1}{2}.\frac{2016}{2017}\)= \(\frac{1008}{2017}< \frac{1008}{2016}=\frac{1}{2}\)
(=) \(S< \frac{1}{2}\)(đpcm)
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S=\(\frac{2}{1X3}\)+\(\frac{2}{3X5}\)+\(\frac{2}{5X7}\)+.....+\(\frac{2}{2015X2017}\)
2016/2017 nhé
k cho mình nha
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2/1*3+2/3*5+2/5*7+...+2/2015*2017
=1-1/3+1/3-1/5+...+1/2015-1/2017
=1-1/2017
=2017/2017-1/2017
=2016/2017
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tính A=\(\frac{1}{2}\left(\frac{1}{1x3}\right)\left(\frac{1}{2x4}\right)\left(\frac{1}{3x5}\right)x....x\left(\frac{1}{2015x2017}\right)\)
Cho S=1/1x3+1/2x4+1/3x5+..............+1/97x99+1/98x100
So sánh S với 1
\(S=\frac{1}{1.3}+\frac{1}{2.4}+\frac{1}{3.5}+...+\frac{1}{97.99}+\frac{1}{98.100}\)
\(S< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{97.98}+\frac{1}{98.99}\)
\(S< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{97}-\frac{1}{98}+\frac{1}{98}-\frac{1}{99}\)
\(S< 1-\frac{1}{99}< 1\)
=> S < 1
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a)2/1x3+2/3x5+2/5x7+...+2/37x99
b)3/1x4+3/+3/4x7+...+3/97x100
c)1x3+3x5+...+47x49
d)1x2x3+2x3x4+...+18x19x20
2)Không tính cụ thể hãy so sánh
a)2013x2017và2015x2015
b)2013x2017và2014x2016
Em cần giải gấp các anh chị giúp em nha
So sánh A và B
A= 2/1x3 + 2/3x5 + 2/5x7 +....+ 2/2003x2005
B=2006/2005
Nhanh mk tk nha
A= 2/1x3 + 2/3x5 + 2/5x7 +... + 2/2003x2005
A= 1 - 1/3 +1/3 - 1/5 + 1/5 - 1/7 + ... + 1/2003 + 1/2005
A= 1 - 1/2005
A= 2004/2005
B= 2006/2005
suy ra A < B
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\(A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2003.2005}\)
\(=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2003}-\frac{1}{2005}\)
\(=1-\frac{1}{2005}=\frac{2004}{2005}\)
\(\Rightarrow A=\frac{2004}{2005},B=\frac{2006}{2005}\)
\(\Rightarrow A< B\)
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19 tháng 3 2023 lúc 13:36
so sánh A và B biết
A=\(\dfrac{1}{2x3}+\dfrac{1}{3x4}+\dfrac{1}{4x5}+...+\dfrac{1}{99x100}\)
B=\(\dfrac{1}{1x3}+\dfrac{1}{3x5}+\dfrac{1}{5x7}+...+\dfrac{1}{97x99}\)
\(A=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}=\dfrac{1}{2}-\dfrac{1}{100}=\dfrac{49}{100}\)
\(B=\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{97\cdot99}\right)\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\)
\(=\dfrac{1}{2}\cdot\dfrac{98}{99}=\dfrac{49}{99}>\dfrac{49}{100}=A\)
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