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NT
6
23 tháng 8 2018
\(\frac{B}{2}=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{100\cdot101}\)
\(\frac{B}{2}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{100}-\frac{1}{101}\)
\(\frac{B}{2}=\frac{100}{101}\)
\(B=\frac{200}{101}\)
MN
1
24 tháng 9 2023
\(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{100\cdot101}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-...+\dfrac{1}{100}-\dfrac{1}{101}\)
\(=1-\dfrac{1}{101}\)
\(=\dfrac{100}{101}\)
ZV
2
17 tháng 6 2016
A=1x2+2x3+3x4+4x5+......+99x100+100x101
3A=1x2x(3-0)+2x3x(4-1)+3x4x(5-2)+4x5x(6-3)+...+99x100x(101-98)+100x101x(102-99)
3A=1x2x3-0x1x2+2x3x4-1x2x3+3x4x5-2x3x4+4x5x6-3x4x5+...+99x100x101-98x99x100+100x101x102-99x100x101
3A=(1x2x3+2x3x4+3x4x5+4x5x6+...+99x100x101+100x101x102)-(0x1x2+1x2x3+2x3x4+3x4x5+...+98x99x100+99x100x101)
3A=100x101x102
A=100x101x102:3
A=343400
17 tháng 6 2016
A = 1x2 + 2x3 + 3x4 + 4x5 + ... + 99x100 + 100x101
3A = 1x2x(3-0) + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98) + 100x101x(102-99)
3A = 1x2x3 - 0x1x2 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100 + 100x101x102 - 99x100x101
3A = 100x101x102 - 0x1x2
3A = 100x101x102
A = 100x101x34
A = 343400
14 tháng 1 2016
\(\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{100.101}=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-....-\frac{1}{101}\)
\(=1-\frac{1}{101}=\frac{101}{101}-\frac{1}{101}=\frac{100}{101}\)
NN
1
14 tháng 8 2016
\(\frac{1}{1x2}x\frac{4}{2x3}x\frac{9}{3x4}x...x\frac{10000}{100x101}=\frac{1x1}{1x2}x\frac{2x2}{2x3}x\frac{3x3}{3x4}x...x\frac{100x100}{100x101}\)
=\(\frac{1x2x3x...x100}{1x2x3x...x100}x\frac{1x2x3x...x100}{2x3x4x...x101}=1x\frac{1}{101}=\frac{1}{101}\)
28 tháng 11 2018
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
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
24 tháng 4 2021
Ta có: \(C=\dfrac{2}{1.2}+\dfrac{2}{2.3}+\dfrac{2}{3.4}+\dfrac{2}{4.5}+\dfrac{2}{5.6}+\dfrac{2}{6.7}\)
\(\Leftrightarrow C=2\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}\right)\)
\(\Leftrightarrow C=2\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}\right)\)
\(\Leftrightarrow C=2\left(1-\dfrac{1}{7}\right)=\dfrac{2.6}{7}=\dfrac{12}{7}\)
(6x + 35 ) = 330 : 6
6x+35=55
6x=55-35
6x=20
x=20:6
x=10/3