1.So sanh A va B
a)A= 20/39 + 22/27 + 18/23
B= 14/39 + 22/29 + 18/41
b)A= 3/83 + 7/84
B= 7/83 + 8/84
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xét A và B,ta thấy:
20/39>14/39
22/27>22/29
18/43<18/41
Ta có: 20/39+22/27>14/39+22/29
2012^2013+2013^2013<2013^2013+2013^2014
xet A va B ta thay:
20/39>14/39
22/27>22/29
18/43<18/41
vay A>B
Ta có: \(\dfrac{20}{39}>\dfrac{20}{41}>\dfrac{18}{41}\left(1\right)\)
\(\dfrac{22}{27}>\dfrac{22}{29}\left(2\right)\)
\(\dfrac{18}{43}=1-\dfrac{25}{43};\dfrac{14}{39}=1-\dfrac{25}{39}\)
Vì \(\dfrac{25}{43}< \dfrac{25}{39}\Rightarrow1-\dfrac{25}{43}>1-\dfrac{25}{39}\Rightarrow\dfrac{18}{43}>\dfrac{14}{39}\left(3\right)\)
Từ \(\left(1\right);\left(2\right);\left(3\right)\) ta suy ra : A>B
a, Ta có:
A= \(\dfrac{3}{8^3}+\dfrac{7}{8^4}=\dfrac{3}{8^3}+\dfrac{3}{8^4}+\dfrac{4}{8^4}\)
B= \(\dfrac{7}{8^3}+\dfrac{3}{8^4}=\dfrac{3}{8^3}+\dfrac{4}{8^3}+\dfrac{3}{8^4}\)
Vì \(\dfrac{4}{8^4}< \dfrac{4}{8^3}\) nên A < B.
b, Ta có:
\(\dfrac{20}{39}>\dfrac{14}{39}\)
\(\dfrac{22}{27}>\dfrac{22}{29}\)
\(\dfrac{18}{43}< \dfrac{18}{41}\)
\(\Rightarrow\)\(\dfrac{20}{39}+\dfrac{22}{27}+\dfrac{18}{43}>\dfrac{14}{39}+\dfrac{22}{29}+\dfrac{18}{41}\)
Hay A > B
Ta thấy :
\(\frac{20}{39}>\frac{14}{39}\)
\(\frac{22}{27}>\frac{22}{29}\)
\(\frac{18}{43}< \frac{18}{41}\)
\(\Rightarrow\frac{20}{39}+\frac{22}{27}+\frac{18}{43}>\frac{14}{39}+\frac{22}{29}+\frac{18}{41}\)
=> A > B