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\(A=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}=\dfrac{1}{2}-\dfrac{1}{100}=\dfrac{49}{100}\)
\(B=\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{97\cdot99}\right)\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\)
\(=\dfrac{1}{2}\cdot\dfrac{98}{99}=\dfrac{49}{99}>\dfrac{49}{100}=A\)
\(A=\frac{9999}{32000}=0,31246875...\)
\(\frac{1}{1000}=0,001\Rightarrow0,31246875...>0,001\)
\(\Rightarrow A>\frac{1}{1000}\)
a) 38 + 41 + 117 + 159 + 62
= ( 38 + 62 ) + ( 41 + 159 ) + 117
= 100 + 200 + 117
= 300 + 117
= 417
b) 42 x 53 + 47 x 156 - 47 x 144
= 47 x ( 156 - 144 ) + 42 x 53
= 47 x 12 + 42 x 53
= 564 + 2226
= 2790
c) 341 x 67 + 341 x 16 + 659 x 83
= 341 x ( 67 + 16 ) + 659 x 83
= 341 x 83 + 659 x 83
= 83 x ( 341 + 659 )
= 83 x 1000
= 83000
hok tốt
1.a)341.67+341.16+659.82
=341.(67+16)+659.82
=341.83+659.82
=341+341.82+659.82
=341+82.(341+659)
=341+82.1000
=82341
b)42.53+47.156-47.114
=42.53+47.(156-114)
=42.53+47.42
=42.(53+47)
=42.100
=4200