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3psilon

  • one year ago

Dad dreamed that he put $1 on the first square,$2 on the second, $4 dollars on the third, and so on, doubling the amount each time.If it costs $65,535 to cover all the squares,how many squares were in Dad's dream?

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  1. satellite73
    • one year ago
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    \[1+2+2^2+2^3+...+2^{n-1}=2^n-65535\]

  2. satellite73
    • one year ago
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    oops i mean \[=2^n-1=65535\]

  3. 3psilon
    • one year ago
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    My book says there are 16 squares but only 1 covered ?

  4. satellite73
    • one year ago
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    yes there are 16

  5. satellite73
    • one year ago
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    \[2^n-1=65535\] \[2^n=65526\] and \[2^{16}=65536\]

  6. satellite73
    • one year ago
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    another typo, \(2^n=65536\)

  7. wio
    • one year ago
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    It's a geometric series, right? So in general we use: \[ \Large \sum_{i=0}^{n-1}a_0r^i = a_0\frac{1-r^n}{1-r} \]

  8. wio
    • one year ago
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    Where \(a_0 = 1\) and \(r=2\)...

  9. nia_2012
    • one year ago
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    65535 = 2^16 - 1 --> 16 squares

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