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A = 1/99 - 1/99.98 - 1/98.97 - ............... - 1/3.2 - 1/2.1
\(A=\frac{1}{99}-\left(\frac{1}{99.98}+\frac{1}{98.97}+...+\frac{1}{3.2}+\frac{1}{2.1}\right)\)
đặt \(B=\frac{1}{99.98}+\frac{1}{97.87}+...+\frac{1}{3.2}+\frac{1}{2.1}\)
\(B=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{97.98}+\frac{1}{98.99}\)
\(B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{97}-\frac{1}{98}+\frac{1}{98}-\frac{1}{99}\)
\(B=1-\frac{1}{99}\)
\(B=\frac{98}{99}\)
\(\Rightarrow A=\frac{1}{99}-\frac{98}{99}=\frac{-97}{99}\)
a) \(\frac{1}{100.99}-\frac{1}{99.98}-\frac{1}{98.97}-...-\frac{1}{3.2}-\frac{1}{2.1}\)
\(=\frac{1}{100.99}-\left(\frac{1}{99.98}+\frac{1}{98.97}+...+\frac{1}{3.2}+\frac{1}{2.1}\right)\)
Đặt A = \(\frac{1}{99.98}+\frac{1}{98.97}+...+\frac{1}{3.2}+\frac{1}{2.1}\)
A = \(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{97.98}+\frac{1}{98.99}\)
A = \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{97}-\frac{1}{98}+\frac{1}{98}-\frac{1}{99}\)
A = \(1-\frac{1}{99}\)
A = \(\frac{98}{99}\)
Thay A vào ta được :
\(\frac{1}{100.99}-\frac{98}{99}=\frac{1}{9900}-\frac{98}{99}=\frac{-9799}{9900}\)
b) \(\frac{\left(1+2+3+...+100\right).\left(\frac{1}{3}-\frac{1}{5}-\frac{1}{7}-\frac{1}{9}\right).\left(6,3.12-3,6.21\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)
Ta thấy biểu thức trong ngoặc thứ ba của tử số có kết quả bằng 0
\(\Rightarrow\)Phân số ấy có kết quả bằng 0
`a, 1/2 +x=3/4`
`=> x= 3/4 -1/2`
`=> x= 3/4-2/4`
`=>x= 1/4`
`b, 5/2 -x=1/3`
`=> x= 5/2 -1/3`
`=> x= 15/6 - 2/6`
`=>x= 13/6`
`c, 2 . (1/3 +x)=1/5`
`=> 1/3 +x=1/5:2`
`=> 1/3 +x= 1/10`
`=>x= 1/10-1/3`
`=>x= 3/30 - 10/30`
`=>x=-7/30`
`d, 2/3 - (1/2 -x)=1/5`
`=> 1/2-x= 2/3 -1/5`
`=>1/2-x= 10/15 - 3/15`
`=>1/2-x=7/15`
`=>x= 1/2-7/15`
`=>x=1/30`
`1/2 + x = 3/4`
`=> x = 3/4 - 1/2`
`=> x = 1/4`
`5/2 - x = 1/3`
`=> x = 5/2 - 1/3`
`=> x = 13/6`
`2.(1/3 + x) = 1/5`
`=>1/3 + x = 1/10 `
`=> x = 1/10 - 1/3`
`=> x = -7/30`
`2/3 - (1/2 -x)= 1/5`
`=> 1/2 - x = 7/15`
`=> x = 1/2 - 7/15`
`=> x = 1/30`
`a, 1/2 +1/3 +1/4`
`= 6/12 + 4/12 + 3/12`
`= (6+4+3)/12`
`= 13/12`
`b,5/2 -1/3 +1/4`
`= 30/12 - 4/12 + 3/12`
`=(30-4+3)/12`
`= 29/12`
`c, 1/2 . 1/3 +1/2 . 2/3`
`= 1/2. (1/3+2/3)`
`= 1/2. 3/3`
`=1/2 .1`
`=1/2`
`d, 3/2 - 1/3 +2/5`
`= 45/30 - 10/30 + 12/30`
`=(45-10+12)/30`
`= 47/30`
1/2 là 12 hả bạn?
Hay sao?