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3psilon
 3 years 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?
3psilon
 3 years 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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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[1+2+2^2+2^3+...+2^{n1}=2^n65535\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oops i mean \[=2^n1=65535\]

3psilon
 3 years ago
Best ResponseYou've already chosen the best response.0My book says there are 16 squares but only 1 covered ?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[2^n1=65535\] \[2^n=65526\] and \[2^{16}=65536\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0another typo, \(2^n=65536\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0It's a geometric series, right? So in general we use: \[ \Large \sum_{i=0}^{n1}a_0r^i = a_0\frac{1r^n}{1r} \]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Where \(a_0 = 1\) and \(r=2\)...

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.065535 = 2^16  1 > 16 squares
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