1/2x1/3+1/4
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1/2x1/3+1/3-1/4+1/4x1/5
= 1/2-1/3+1/3-1/4+1/4-1/5
=1/2-1/5
=3/10. (1/2x1/3= 1/2x3)
1/2x1/3+1/3-1/4+1/4x1/5 = 1/2-1/3+1/3-1/4+1/4-1/5 =1/2-1/5 =3/10. (1/2x1/3= 1/2x3)
`1/5xx1/2:3/10`
`=1/10xx10/3`
`=1/3`
`1/2xx1/3:1/4`
`=1/6xx4/1`
`=2/3`
a) \(\dfrac{1}{5}\times\dfrac{1}{2}:\dfrac{3}{10}=\dfrac{1}{5}\times\dfrac{1}{2}\times\dfrac{10}{3}=\dfrac{1\times1\times10}{5\times2\times3}=\dfrac{10}{30}=\dfrac{1}{3}\)
b) \(\dfrac{1}{2}\times\dfrac{1}{3}:\dfrac{1}{4}=\dfrac{1}{2}\times\dfrac{1}{3}\times4=\dfrac{1\times1\times4}{2\times3}=\dfrac{4}{6}=\dfrac{2}{3}\)
\(\frac{1}{1}\cdot\frac{1}{2}+\frac{1}{2}\cdot\frac{1}{3}+\frac{1}{3}\cdot\frac{1}{4}+...+\frac{1}{79}\cdot\frac{1}{80}\)
\(=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{79\cdot80}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}+...+\frac{1}{79}-\frac{1}{80}\)
\(=1-\frac{1}{80}\)
\(=\frac{79}{80}\)
x + 1/2 x 1/3 = 3/4
x + 1/6 = 3/4
x = 3/4 - 1/6
x = 7/12
(1-1/2x1/2)x(1-1/3x1/3)x(1-1/4x1/4)x…x(1-1/2007x1/2007) = ( 1 - 1/4 ) x ( 1 - 1/9 ) x ( 1- 1/16) x .....x ( 1 - 1/4028049) = 3/4 x 8/9 x 15/16 x .....x 4028048 / 4028049 = 3 x 8 x 15 x .....x 4028048 / 4 x 9 x 16 x ......x 4028049 = 1 x 3 x 2 x 4 x 3 x 5 x .....x 2006 x 2008 / 2x2 x 3 x3 x 4 x 4 x .....x 2007 x 2007 = ( 1 x 2 x 3 x .....x 2006) x ( 3 x 4 x 5 x .....x 2008) / ( 2 x 3 x 4 x ....x 2007) x ( 2 x 3 x 4 x ....x 2007) = 2008 / 2007 x 2 = 1004 / 2007
(1-1/2x1/2)x(1-1/3x1/3)x(1-1/4x1/4)x…x(1-1/2007x1/2007)
= ( 1 - 1/4 ) x ( 1 - 1/9 ) x ( 1- 1/16) x .....x ( 1 - 1/4028049)
= 3/4 x 8/9 x 15/16 x .....x 4028048 / 4028049
= 3 x 8 x 15 x .....x 4028048 / 4 x 9 x 16 x ......x 4028049
= 1 x 3 x 2 x 4 x 3 x 5 x .....x 2006 x 2008 / 2x2 x 3 x3 x 4 x 4 x .....x 2007 x 2007
= ( 1 x 2 x 3 x .....x 2006) x ( 3 x 4 x 5 x .....x 2008) / ( 2 x 3 x 4 x ....x 2007) x ( 2 x 3 x 4 x ....x 2007)
= 2008 / 2007 x 2
= 1004 / 2007
= 1/6 + 1/4
= 5/12
\(\frac{1}{2}\times\frac{1}{3}+\frac{1}{4}=\frac{1}{6}+\frac{1}{4}\)
\(=\frac{5}{12}\)