Quod Erat Demonstrandum

2013/06/16

錯在哪裡之 1 不大於 1/2

Filed under: Fun — johnmayhk @ 11:12 下午

易知

1

=\frac{1\times 2}{2}

=\frac{1\times 2\times 3}{2\times 3}

=\frac{1\times 2\times 3\times 4\times\dots}{2\times 3\times 4\times 5\times\dots}

\frac{1\times 2\times 3\times 4\times\dots}{2\times 3\times 4\times 5\times\dots}

=\frac{1}{2}(\frac{2}{3})(\frac{3}{4})(\frac{4}{5})\dots

\le \frac{1}{2}

1\le \frac{1}{2}

5 則迴響 »

  1. 分子多分母一項?

    迴響 由 Marcus — 2013/06/17 @ 11:50 上午 | 回覆

  2. 錯在
    無限/無限

    迴響 由 SZELONG — 2013/06/18 @ 4:14 下午 | 回覆

  3. You cannot change the order of multiplication or division when it is an infinite product. The third equality is wrong.

    迴響 由 Mark Shea — 2013/06/19 @ 12:02 上午 | 回覆

  4. 0
    =0+0+0+…
    =(1-1)+(1-1)+(1-1)+…
    =1-1+1-1+1-1+…
    =1-(1-1)-(1-1)-(1-1)…
    =1-0-0-0…
    =1

    迴響 由 Yee — 2013/06/25 @ 8:29 下午 | 回覆

  5. The infinite product does not converge absolutly.

    迴響 由 forretrio — 2013/06/30 @ 1:27 下午 | 回覆


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