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Dễ mà bạn:
a) Cho A=1/100-1/100.99-1/99.98-...-1/3.2-1/2.1
\(A=\frac{1}{100}-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{98.99}+\frac{1}{99.100}\right)\)
\(A=\frac{1}{100}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)\)
\(A=\frac{1}{100}-\left(1-\frac{1}{100}\right)=\frac{1}{100}-\frac{99}{100}=-\frac{98}{100}=-\frac{49}{50}\)
b) \(-15,5.20,8+3,5.9,2-15,5.9,2+3,5.20,8=-15,5.\left(20,8+9,2\right)+3,5\left(9,2+20,8\right)\)
\(=-15,5.30+3,5.30=30\left(3,5-15,5\right)=30.\left(-12\right)=-360\)
e) \(\frac{1}{100}-\frac{1}{100.99}-\frac{1}{99.98}-...-\frac{1}{3.2}-\frac{1}{2.1}\)
\(=\frac{1}{100}-\left(\frac{1}{100.99}+\frac{1}{99.98}+...+\frac{1}{3.2}+\frac{1}{2.1}\right)\)
\(=\frac{1}{100}-\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)\)
\(=\frac{1}{100}-\left(1-\frac{1}{100}\right)\)
\(=\frac{1}{100}-\frac{99}{100}\)
\(=\frac{-98}{100}\)\
\(=\frac{-49}{50}\)
g)-15,5 . 20,8 + 3,5.9,2 - 15,5.9,2 + 3,5.20,8
=20,8.(-15.5+3,5)+9,2(-15.5+3.5)
=(-15.5+3.5)(20.8+9.2)
=(-12).30
=-360
a: \(=\dfrac{1.3-1.6}{2.6}-\dfrac{5}{6}:2\)
\(=-\dfrac{3}{26}-\dfrac{5}{12}\)
\(=\dfrac{-83}{156}\)
b: \(=20.8\left(-15.5+3.5\right)+9.2\left(3.5-15.5\right)\)
\(=-12\left(20.8+9.2\right)\)
\(=-12\cdot30=-360\)
\(=-15.5\left(20.8+9.2\right)+3.5\left(9.2+20.8\right)\)
\(=30\cdot\left(-15.5+3.5\right)\)
\(=-12\cdot30=-360\)
1/100-1/100.99-1/99.98-.....1/3.2-1/2.1
= 1/100-(1/100.99+1/99.98+.....+1/3.2+1/2.1)
=1/100-(1/1-1/2+1/2-1/3+...+1/98-1/99+1/99-1/100)
=1/100-(1/1-1/100)
=1/100-99/100
=-98/100
=-49/50
\(A=\frac{1}{100}-\frac{1}{100.99}-\frac{1}{99.98}-...-\frac{1}{3.2}-\frac{1}{2.1}\)
\(=\frac{1}{100}-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{98.99}+\frac{1}{99.100}\right)\)
\(=\frac{1}{100}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)\)
\(\frac{1}{100}-\left(1-\frac{1}{100}\right)=\frac{1}{100}+\frac{1}{100}-1=\frac{1}{50}-1=-\frac{49}{50}\)
