1/20x19 - 1/19x18 - 1/18x17 - ... - 1/3x2 - 1/2x1
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AD
1
9 tháng 4 2018
Ta có : \(\frac{1}{2010.2009}-\frac{1}{2009.2008}-\frac{1}{2008.2007}-.....-\frac{1}{3.2}-\frac{1}{2.1}\)
\(=\frac{1}{2010.2009}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{2008.2009}\right)\)
\(=\frac{1}{2010.2009}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+......+\frac{1}{2008}-\frac{1}{2009}\right)\)
\(=\frac{1}{2010.2009}-\left(1-\frac{1}{2009}\right)\)
\(=\frac{1}{2010.2009}-1+\frac{1}{2009}=\frac{1}{2010.2009}-\frac{2010.2009}{2010.2009}+\frac{2010}{2010.2009}\)
\(=\frac{1-2010.2009+2010}{2009.2010}=\frac{-4036079}{4038090}\)
17 tháng 9 2018
Đặt \(A=\frac{1}{99.98}-...-\frac{1}{3.2}-\frac{1}{2.1}\)
\(-A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{98.99}\)
\(-A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}\)
\(-A=1-\frac{1}{99}\)
\(-A=\frac{98}{99}\)
\(A=\frac{-98}{99}\)
Chúc bạn học tốt ~
LH
17 tháng 9 2018
Đặt A = \(\frac{1}{99.98}-...-\frac{1}{3.2}-\frac{1}{2.1}\)
=> - A = \(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{98.99}\)
- A = \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}\)
- A = \(1-\frac{1}{99}\)
- A = \(\frac{98}{99}\)
=> A = \(-\frac{98}{99}\)
Vậy A = \(-\frac{98}{99}\)
Hok tốt
PL
0
28 tháng 8 2018
-1/(1999.2000)= 1/2000-1/1999 ...... -1/2= 1/2-1
Vậy A= 1/2000-1/1999 +1/1999-1/1998+....+1/3-1/2+1/2-1 = -1+1/2000= -1999/2000
LC
1
5 tháng 9 2015
Đặt A = \(\frac{1}{99}-\frac{1}{99.98}-.....-\frac{1}{2.1}\)
\(A=\frac{1}{99}-\left[-\left(\frac{1}{1.2}+\frac{1}{2.3}+.....+\frac{1}{98.99}\right)\right]\)
\(A=\frac{1}{99}+\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-.....-\frac{1}{99}\right)\)
\(A=\frac{1}{99}+\left(1-\frac{1}{99}\right)\)
\(A=\frac{1}{99}+\frac{98}{99}=1\)
BT
1
N
11 tháng 6 2017
\(\frac{1}{100.99}-\frac{1}{99.98}-......-\frac{1}{3.2}-\frac{1}{2.1}\)
\(=-\left(-\frac{1}{100.99}+\frac{1}{99.98}+...........+\frac{1}{3.2}+\frac{1}{2.1}\right)\)
\(=-\left(-\frac{1}{100}-\frac{1}{99}+\frac{1}{99}-\frac{1}{98}+......+\frac{1}{3}-\frac{1}{2}+\frac{1}{2}-1\right)\)
\(=-\left(-\frac{1}{100}-1\right)\)
\(=\frac{1}{100}+1\)
\(=\frac{101}{100}\)
NT
3
LN
Lưu Nguyễn Hà An
CTVHS
VIP
16 tháng 9 2023
Uk, Long cứ đợi ng ta trả lời xong long làm giống là đc ý mà!
NT
3
N
25 tháng 8 2018
\(C=\frac{1}{100}-\left(\frac{1}{100.99}+\frac{1}{99.98}+...+\frac{1}{3.2}+\frac{1}{2.1}\right)\)
\(C=\frac{1}{100}-\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\right)\)
\(C=\frac{1}{100}-\left(1-\frac{1}{100}\right)\)
\(C=\frac{1}{100}-\frac{99}{100}\)
\(C=-\frac{98}{100}=-\frac{49}{50}\)
25 tháng 8 2018
\(C=\frac{1}{100}-\frac{1}{100.99}-\frac{1}{99.98}-\frac{1}{98.97}-...-\frac{1}{3.2}-\frac{1}{2.1}\)
\(=\frac{1}{100}-\left(\frac{1}{100.99}+\frac{1}{99.98}+\frac{1}{98.97}+....+\frac{1}{3.2}+\frac{1}{2.1}\right)\)
\(=\frac{1}{100}-\left(\frac{1}{100}-\frac{1}{99}+\frac{1}{99}-\frac{1}{98}+\frac{1}{98}-\frac{1}{97}+...+\frac{1}{3}-\frac{1}{2}+\frac{1}{2}-1\right)\)
\(=\frac{1}{100}-\left(\frac{1}{100}-1\right)\)
\(=1\)
\(\dfrac{1}{20\times19}\) - \(\dfrac{1}{19\times18}\) - \(\dfrac{1}{18\times17}\) - ... - \(\dfrac{1}{3\times2}\) - \(\dfrac{1}{2\times1}\)
= \(\dfrac{1}{20\times19}\) - (\(\dfrac{1}{19\times18}\) + \(\dfrac{1}{18\times17}\) + ... + \(\dfrac{1}{3\times2}\) + \(\dfrac{1}{2\times1}\))
= \(\dfrac{1}{20\times19}\) - (\(\dfrac{1}{1\times2}\) + \(\dfrac{1}{2\times3}\) + ... + \(\dfrac{1}{17\times18}\) + \(\dfrac{1}{18\times19}\))
= \(\dfrac{1}{380}\) - (\(\dfrac{1}{1}\) - \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + ... + \(\dfrac{1}{17}\) - \(\dfrac{1}{18}\) + \(\dfrac{1}{18}\) - \(\dfrac{1}{19}\))
= \(\dfrac{1}{380}\) - (\(\dfrac{1}{1}\) - \(\dfrac{1}{19}\))
= \(\dfrac{1}{380}\)- \(\dfrac{18}{19}\)
= - \(\dfrac{359}{380}\)
\(\dfrac{1}{20\cdot19}-\dfrac{1}{19\cdot18}-\dfrac{1}{18\cdot17}-...-\dfrac{1}{3\cdot2}-\dfrac{1}{2\cdot1}\)
\(=\left(\dfrac{1}{19}-\dfrac{1}{20}\right)-\left(\dfrac{1}{18}-\dfrac{1}{19}\right)-\left(\dfrac{1}{17}-\dfrac{1}{18}\right)-...-\left(\dfrac{1}{2}-\dfrac{1}{3}\right)-\left(1-\dfrac{1}{2}\right)\)
\(=\dfrac{1}{19}-\dfrac{1}{20}-\dfrac{1}{18}+\dfrac{1}{19}-\dfrac{1}{17}+\dfrac{1}{18}-...-\dfrac{1}{2}+\dfrac{1}{3}-1+\dfrac{1}{2}\)
\(=-\dfrac{1}{20}+\left(\dfrac{1}{19}+\dfrac{1}{19}\right)+\left(-\dfrac{1}{18}+\dfrac{1}{18}\right)+\left(-\dfrac{1}{17}+\dfrac{1}{17}\right)+...+\left(-\dfrac{1}{3}+\dfrac{1}{3}\right)+\left(-\dfrac{1}{2}+\dfrac{1}{2}\right)-1\)
\(=-\dfrac{1}{20}+\dfrac{2}{19}-1\)
\(=-\dfrac{359}{380}\)