2/1x2+2/2x3+2/3x4+....+2/1999x2000
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PN
30 tháng 8 2015
Đặt A=1x2+2x3+3x4+.......+1999x2000
3xA=1x2x3+2x3x3+3x4x3+...........+1999x2000x3
3xA=1x2x3+2x3x(4-1)+............+1999x2000x(2001-1998)
3xA=1x2x3+2x3x4-1x2x3+...........+1999x2000x2001-1998x1999x2000
3xA=1999x2000x2001
A=1999x2000x2001:3
A=2666666000
BI
1
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
13 tháng 8 2023
B = \(\dfrac{2}{1\times2}\) + \(\dfrac{2}{2\times3}\)+ \(\dfrac{2}{3\times4}\)+...+ \(\dfrac{2}{99\times100}\)
B = 2 \(\times\) ( \(\dfrac{1}{1\times2}\) + \(\dfrac{1}{2\times3}\)+ \(\dfrac{1}{3\times4}\)+....+ \(\dfrac{1}{99\times100}\))
B = 2 \(\times\) ( \(\dfrac{1}{1}\) - \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\)+...+ \(\dfrac{1}{99}\) - \(\dfrac{1}{100}\))
B = 2 \(\times\) ( \(\dfrac{1}{1}\) - \(\dfrac{1}{100}\))
B = 2 \(\times\) \(\dfrac{99}{100}\)
B = \(\dfrac{99}{50}\)
26 tháng 1 2018
A = 2 x ( 1/1x2 + 1/2x3 +.....+ 1/9x10 )
= 2 x ( 1 - 1/2 + 1/2 - 1/3 + ..... + 1/9 - 1/10 )
= 2 x ( 1 - 1/10 )
= 2 x 9/10
= 9/5
Tk mk nha
DN
26 tháng 1 2018
2. 2. 2. 2. 2
A=---- + ----- + ------ + ------ +......+ -------
1.2. 2.3. 3.4. 4.5. 9.10
2( 1. 1. 1. 1. )
= --------- + --------- + --------- +....+ ----------
1.2 2.3 3.4. 9.10
= 2.(1-1/2+1/2-1/3+1/3-1/4+...+1/9-1/10)
=2.(1-1/10)
=2.9/10
=9/5
TT
4
DP
15 tháng 7 2017
Đặt \(A=\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+....+\frac{2}{18.19}+\frac{2}{19.20}\)
\(A=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\right)\)
\(A=2\left(1-\frac{1}{20}\right)\)
\(A=2.\frac{19}{20}=\frac{19}{10}\)
Q
15 tháng 7 2017
\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{18.19}+\frac{2}{19.20}\)
\(=2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{18.19}+\frac{1}{19.20}\right)\)
\(=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\right)\)
\(=2\left(1-\frac{1}{20}\right)\)
\(=2.\frac{19}{20}\)
\(=\frac{19}{10}\)
24 tháng 4 2021
Ta có: \(C=\dfrac{2}{1.2}+\dfrac{2}{2.3}+\dfrac{2}{3.4}+\dfrac{2}{4.5}+\dfrac{2}{5.6}+\dfrac{2}{6.7}\)
\(\Leftrightarrow C=2\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}\right)\)
\(\Leftrightarrow C=2\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}\right)\)
\(\Leftrightarrow C=2\left(1-\dfrac{1}{7}\right)=\dfrac{2.6}{7}=\dfrac{12}{7}\)
HV
0
BT
11 tháng 3 2017
A=2(\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\))=2(\(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\))
=> A=2(\(\frac{1}{1}-\frac{1}{100}\))=2.\(\frac{99}{100}=\frac{99}{50}\)
ĐS: A=99/50
11 tháng 3 2017
\(\frac{2}{1\times2}+\frac{2}{2\times3}+\frac{2}{3\times4}+\frac{2}{4\times5}+...+\frac{2}{99\times100}\)
\(=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{99\times100}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)
\(=\frac{1}{1}-\frac{1}{100}\)
\(=\frac{99}{100}\)
HV
3
15 tháng 1 2022
\(\Leftrightarrow y\cdot\dfrac{99}{50}=\dfrac{198}{100}=\dfrac{99}{50}\)
hay y=1
easy mà
=2.(1/1.2+1/2.3+...+1/1999.2000)
=2.(1/1-1/2+1/2-1/3+....1/1999-1/2000)
=2.(1-1/2000)
=2.1999/2000
=3998/2000=... tự rút gọn :D
2. là nhân à