a. -1/2+1/3-1/4
tính chi tiết giúp mình nhé
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a)
`9/2-3`
`=9/2-6/2`
`=3/2`
b)
`8/5xx25/12`
`=10/3`
c)
`4:3/7`
`=4xx7/3`
`=28/3`
1/3 - 1/4 = 4/12 - 3/12 = 1/12
2/7 . 14/5 - 1 = 2.14/7.5 - 1 =4/5 - 1 = -1/5
3/4 - 1/25 x 5 = 3/4 - 1.5/25.1 = 3/4 - 1/5 = 11/20
-8 . ( 6. 1/24 ) = -8 . ( 6.1/24.1 ) = -8 . 1/4 = -8 . 1/4.1 = -2
Ta có :
\(S=\left(1+\frac{1}{3}+..+\frac{1}{2011}+\frac{1}{2013}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2012}\right)\)
\(=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2012}+\frac{1}{2013}\right)-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2012}\right)\)
\(=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2012}+\frac{1}{2013}\right)-\left(1+\frac{1}{2}+...+\frac{1}{1006}\right)\)
\(=\frac{1}{1007}+\frac{1}{1008}+...+\frac{1}{2013}=P\)
\(\Rightarrow\left(s-p\right)^{2013}=0^{2013}=0\)
A= 1/3 + 1/3^2 + ... + 1/3^8
3A= 3. (1/3+ 1/3^2+ ... + 1/3^8)
3A=1+ 1/3 + 1/3^2+ ... +1/3^7
=> 3A - A= (1 + 1/3 + 1/3^2 + ... + 1/3^7) - (1/3 + 1/3^2+ ... + 1/3^8)
=> 2A= 1 - 1/ 3^8
2A= 6560/6561
A= 6560/6561 : 2
A= 3280/6561
\(A=\frac{1\times111+2\times110+3\times109+...+111\times1}{1+\left(1+2\right)+\left(1+2+3\right)+...+\left(1+2+3+...+111\right)}\)
\(A=\frac{1\times111+2\times110+3\times109+...+111\times1}{\left(1+1+...+1\right)+\left(2+2+...+2\right)+...+111}\)(\(111\)số hạng \(1\), \(110\)số hạng \(2\),...)
\(A=\frac{1\times111+2\times110+3\times109+...+111\times1}{1\times111+2\times110+3\times109+...+111\times1}\)
\(A=1\)
-1/2 + 1/3 - 1/4
= -12/24 + 8/24 - 6/24
= -10/24 rút gọn => -5/12