tính nhanh nha mn A = 1\4 + 1\8 + 1\16 + 1\32 + 1\64 + 1\128 + 1\256 + 1\512 10/09/2021 Bởi aihong tính nhanh nha mn A = 1\4 + 1\8 + 1\16 + 1\32 + 1\64 + 1\128 + 1\256 + 1\512
Ta có: $A=\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}+\dfrac{1}{128}+\dfrac{1}{256}+\dfrac{1}{512}$ $A\times2=2\times(\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}+\dfrac{1}{128}+\dfrac{1}{256}+\dfrac{1}{512})$ $A\times2=\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}+\dfrac{1}{128}+\dfrac{1}{256}$ $A\times2-A=(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}+\dfrac{1}{128}+\dfrac{1}{256})-(\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}+\dfrac{1}{128}+\dfrac{1}{256}+\dfrac{1}{512})$ $A=\dfrac{1}{2}-\dfrac{1}{512}$ $A=\dfrac{255}{512}$ Bình luận
Ta có:
$A=\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}+\dfrac{1}{128}+\dfrac{1}{256}+\dfrac{1}{512}$
$A\times2=2\times(\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}+\dfrac{1}{128}+\dfrac{1}{256}+\dfrac{1}{512})$
$A\times2=\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}+\dfrac{1}{128}+\dfrac{1}{256}$
$A\times2-A=(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}+\dfrac{1}{128}+\dfrac{1}{256})-(\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}+\dfrac{1}{128}+\dfrac{1}{256}+\dfrac{1}{512})$
$A=\dfrac{1}{2}-\dfrac{1}{512}$
$A=\dfrac{255}{512}$
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