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=(48/49) x (63/64) x (80/81) x (99/100) x (120/121) x (143/144)
=(6x8/7x7) x (7x9/8x8) x (8x10/9x9) x (9x11/10x10) x (10x12/11x11) x (11x13/12x12)
=\(\frac{6x8x8x10x10x12x7x9x9x11x11x13}{7x7x8x8x9x9x10x10x11x11x12x12}\)
rút gọn đi còn: 13/14
Bài 1:
a; (\(\dfrac{1}{4}\)\(x\) - \(\dfrac{1}{8}\)) x \(\dfrac{3}{4}\) = \(\dfrac{1}{4}\)
\(\dfrac{1}{4}x\) - \(\dfrac{1}{8}\) = \(\dfrac{1}{4}\) : \(\dfrac{3}{4}\)
\(\dfrac{1}{4}\)\(x\) - \(\dfrac{1}{8}\) = \(\dfrac{1}{4}\) x \(\dfrac{4}{3}\)
\(\dfrac{1}{4}x\) - \(\dfrac{1}{8}\) = \(\dfrac{1}{3}\)
\(\dfrac{1}{4}x\) = \(\dfrac{1}{3}\) + \(\dfrac{1}{8}\)
\(\dfrac{1}{4}\) \(x\)= \(\dfrac{8}{24}\) + \(\dfrac{11}{24}\)
\(\dfrac{1}{4}x=\dfrac{11}{24}\)
\(x=\dfrac{11}{24}:\dfrac{1}{4}\)
\(x=\dfrac{11}{24}\times4\)
\(x=\dfrac{11}{6}\)
b; \(\dfrac{12}{5}:x\) = \(\dfrac{14}{3}\) x \(\dfrac{4}{7}\)
\(\dfrac{12}{5}\) : \(x\) = \(\dfrac{8}{3}\)
\(x\) = \(\dfrac{12}{5}\) : \(\dfrac{8}{3}\)
\(x\) = \(\dfrac{12}{5}\) x \(\dfrac{3}{8}\)
\(x\) = \(\dfrac{9}{10}\)
a) ta thấy 1/2x3 + 1/3x4 + 1/4 x 5 + ...... + 1/a x ( a + 1 ) = 1/2 - 1/3 + 1/3 -1/4 +............+ 1/a - 1/a+1 = 49/100
1/2 - 1/a+1= 49/100
1/a+1=1/2 - 49/100
1/a + 1= 1/100
a + 1= 100
a= 100 - 1
a= 99
b) ( 1 - 1/4 ) x ( 1 - 1/9 ) x ( 1 - 1/16) x ..... x (1 - 1/625)
= 3/4 x 8/9 x 15/16 x...........x 575/576x 624/625 = 1x3/1x4 x 2x4/ 3x3 x 3x5/4 x 4x.................x 23x 25/ 24 x 24 x 24x26/ 25x25
= ( 1/1 x 2/3 x 3/4 x 4/5 x .................x 23/24 x 24/25= 1x2x3x4x..............23x24/ 1 x 3 x 4 x5x............24x25=2/25)
( 3/5 x 4/3 x 5/4 x 6/5x.............x 25/24 x 26/25= 3 x 4 x 5x 6 x ............x 25x 26/ 5 x 3 x 4 x 5x............x 24 x 25= 26/5)
2/25 x 26/5= 52/30= 26/25
bài 1"
121/27 x 54/11 < n < 100/21 : 25/126
=> 22 < n < 24
mà n là số tự nhiên
=> n = 23
Bài 2:
(m:1 - m x 1) : ( m x 2005 + m + 1)
= (m-m) : ( m x 2005 + m + 1)
= 0 : (m x 2005 + m + 1) = 0
1.
\(\frac{121}{27}\times\frac{54}{11}< n< \frac{100}{21}:\frac{25}{126}\)
=> \(22< n< 24\)
Mà n là số tự nhiên
=> n = 23
2.
( m : 1 + m x 1 ) : ( m x 2005 + m + 1 )
= ( m - m ) : ( m x 2005 + m + 1 )
= 0 : ( m x 2005 + m + 1 )
= 0