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\(A=\frac{1990^{10}+1}{1990^{11}+1};B=\frac{1990^{11}+1}{1990^{12}+1}\)
Ta có:
\(A=\frac{10\cdot\left(1990^{10}+1\right)}{10\cdot\left(1990^{11}+1\right)}\)
\(\Rightarrow A=\frac{1990^{11}+10}{1990^{12}+10}\)
\(\Rightarrow A=\frac{1990^{11}+1+9}{1990^{12}+1+9}\)
\(\Rightarrow A< B\)
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199010 + 19909 = 19909 ( 1990 + 1 ) = 19909 .1991
199110 = 19919 . 1991
-> 19909 . 1991 < 19919 . 1991
Vậy 199010 + 19909 < 199110
Tk cho mk nếu đúng nhé
Ta co : 199010 + 19909(1990+1)=19909*1991
199110=1999*1991
=> 19909*1991<19919 * 1991
Vay 199010+ 19909<199110
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Lời giải:
$A=1990^{10}+1990^9=1990^9(1990+1)=1990^9.1991< 1991^9.1991=1991^{10}$
Hay $A< B$
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ta có A= 1990^10+1990^9
suy ra A=1990^9 . ( 1990 + 1) = 1990^9 . 1991 mà ta có B= 1991^10 = 1991^9 . 1991
vì 1990^9 < 1991^9 suy ra A<B.chú ý dấu" . " là dấu nhân
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