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(x+1)+(x+2)+(x+3)+(x+4)=110
(x+x+x+x)+(1+2+3+4)=110
4x+10=110
4x=110-10
4x=100
x=100:4
x=25
[ x + 1 ] + [ x + 2 ] + [ x + 3 ] + [ x + 4 ] = 110
=> x + 1 + x + 2 + x + 3 + x + 4 = 110
=> ( x + x + x + x ) + ( 1 + 2 + 3 + 4 ) = 110
=> 4x + 10 = 110
=> 4x = 100
=> x = 25
\(\left(1-\frac{1}{3}\right)x\left(1-\frac{1}{4}\right)x...x\left(1-\frac{1}{2014}\right)\)
A = \(\frac{2}{3}x\frac{3}{4}x\frac{4}{5}x...x\frac{2012}{2013}x\frac{2013}{2014}\)
A = \(\frac{2x3x4x...x2012x2013}{3x4x5x...x2013x2014}\)
a = \(\frac{2}{2014}=\frac{1}{1007}\)
a) 0,1 + 0,2 + 0,3 + 0,4 + ... + 1,9
= ( 1,9 + 0,1 ) x 19 : 2
= 2 x 19 : 2
= 19
b) (1999 x 1998 + 1998 + 1997) x ( 1 + 1/2 : 1 1/2 - 1 1/3)
= (1999 x 1998 + 1998 + 1997) x 0
= 0
\(1\frac{1}{7}\cdot1\frac{1}{8}\cdot1\frac{1}{9}\cdot...\cdot1\frac{1}{50}\)
\(=\frac{8}{7}\cdot\frac{9}{8}\cdot\frac{10}{9}\cdot...\cdot\frac{51}{50}\)
\(=\frac{8\cdot9\cdot10\cdot...\cdot51}{7\cdot8\cdot9\cdot...\cdot50}\)
\(=\frac{51}{7}\)
3/4 x 8/9 x 15/16 x ... x 99/100 x 120/121 = 3 x 8 x 15 x 99 x 120/ 4 x 9 x 16 x 100 x 121
= ( 1 x 3 ) x ( 2 x 4 ) x ( 3 x 5 ) x ... x ( 9 x 11 ) x ( 10 x 12 ) / ( 2 x 2 ) x ( 3 x 3 ) x ( 4 x 4 ) x ... x ( 10 x 10 ) x ( 11 x 11 )
= ( 1 x 2 x 3 x ... x 10 ) x ( 3 x 4 x 5 x ... x 12 ) / ( 2 x 3 x ... x 11 ) x ( 2 x 3 x ... x 11 ) = 12/11x2 = 6/11
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=1/2x2/3x/3/4/.................x2003/2004
= 1x2x3x................x2003
___________________
2x3x4x................x 2004
=1/2004
1. A = { 16; 17; 18; 19; 20; 21; 22; 23; 24 }
2. 245x11+245x38+245x50+245
= 245x11+245x38+245x50+245 x 1
= 245 x ( 11 + 38 + 50 + 1)
= 245 x 100
= 24500
D=1/2-1/32=15/32
E=1/1X2+1/2X3+1/3X4+1/4X5+1/5X6
E=1/1-1/6=5/6
K MÌNH NHA
S=1/2x 2/3x 3/4x............x2016/2017
S=1/1x 1/2017
S=1/2017
\(S=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).....\left(1-\frac{1}{2017}\right)\)
\(S=\frac{1}{2}\cdot\frac{2}{3}\cdot\cdot\cdot\cdot\cdot\cdot\cdot\frac{2016}{2017}\)
\(S=\frac{1.2........2016}{2.3..........2017}\)
\(S=\frac{1}{2017}\)