Question

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?

Answer 1

\[1+2+2^2+2^3+...+2^{n-1}=2^n-65535\]

Answer 2

oops i mean
\[=2^n-1=65535\]

Answer 3

My book says there are 16 squares but only 1 covered ?

Answer 4

yes there are 16

Answer 5

\[2^n-1=65535\]
\[2^n=65526\] and
\[2^{16}=65536\]

Answer 6

another typo, \(2^n=65536\)

Answer 7

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

Answer 8

Where \(a_0 = 1\) and \(r=2\)...

Answer 9

65535 = 2^16 - 1
--> 16 squares