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Math Help - Three students and bread

  1. #1
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    Three students and bread

    Three students share a bread. The first eats half, the second eats half of what is left, and the third eats half of that and so on....How much does each eat?
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by zhupolongjoe View Post
    Three students share a bread. The first eats half, the second eats half of what is left, and the third eats half of that and so on....How much does each eat?
    student 1 = \frac{1}{2}+\frac{1}{16}+\frac{1}{64}+...=\frac{1}  {2^1}+\frac{1}{2^4}+\frac{1}{2^7}+...=\sum_{n=0}^{  \infty}\frac{1}{2^{3n+1}}=

    \frac{1}{2}\sum_{n=0}^{\infty}\frac{1}{8^n}=\frac{  1}{2}\left( \frac{1}{1-\frac{1}{8}}\right)=\frac{1}{2} \left( \frac{1}{\frac{7}{8}}\right)=\frac{1}{2} \cdot \frac{8}{7}=\frac{4}{7}

    You will find a similar pattern for students 2 and 3.

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  3. #3
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    The fractions consumed by each



    1 are 1/2 , 1/16 1/128 totalling ˝[1+(1/8) + (1/8)2 +…]

    2 are 1/4 , 1/32, 1/256 totalling 1/4[1+(1/8) + (1/8)2 +…]

    3 are 1/8, 1/64 1/512, totalling 1/8[1+(1/8) + (1/8)2 +…]


    [1+(1/8) + (1/8)2 +…] = 1 / (1-1/8) = (8/7). Therefore,


    1 consumes (1/2) (8/7) = 4/7

    2 consumes (1/4) (8/7) = 2/7

    3 consumes (1/8) (8/7) = 1/7

    Note 4/7 + 2/7 + 1/7 = 1
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