Cho \(U = \frac{{1.3.5 \ldots .39}}{{21.22.23 \ldots 40}};\quad V = \frac{1}{{{2^{20}} - 1}}.\)Khẳng định nào đúng.
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Lời giải:
Báo sai\(\begin{aligned} &U=\frac{1.3 .5 \ldots 37.39}{(21.23 .25 \ldots .39)(22.24 .26 \ldots .40)}=\frac{1.3 .5 .7 \ldots 37.39}{(21.23 .25 \ldots .39) 2^{10}(11.12 .13 \ldots .20)} \\ &U=\frac{1.3 .5 \ldots 39}{2^{10}(21.23 \ldots .39)(11.13 \ldots 19)(12.14 .16 .18 .20)}=\frac{1.3 .5 . .39}{2^{10} \cdot(11.13 \ldots 39) 2^{5}(6.7 .8 .9 .10)} \\ &U=\frac{1.3 .5 . .39}{2^{15}(7.9 .11 \ldots .39) \cdot(6.8 .10)}=\frac{1.3 .5 \ldots 39}{2^{15} \cdot(7.9 \ldots 39) .2^{5} \cdot 3.5}=\frac{1.3 .5 . .39}{2^{20} \cdot 3.5 .7 \ldots 39}=\frac{1}{2^{20}} \\ &\text { mà } \frac{1}{2^{20}}<\frac{1}{2^{20}-1}=>U<V \end{aligned}\)
