Here's the question you clicked on:
3psilon
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?
\[1+2+2^2+2^3+...+2^{n-1}=2^n-65535\]
oops i mean \[=2^n-1=65535\]
My book says there are 16 squares but only 1 covered ?
\[2^n-1=65535\] \[2^n=65526\] and \[2^{16}=65536\]
another typo, \(2^n=65536\)
It's a geometric series, right? So in general we use: \[ \Large \sum_{i=0}^{n-1}a_0r^i = a_0\frac{1-r^n}{1-r} \]
Where \(a_0 = 1\) and \(r=2\)...
65535 = 2^16 - 1 --> 16 squares