## 3psilon 2 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?

1. satellite73

$1+2+2^2+2^3+...+2^{n-1}=2^n-65535$

2. satellite73

oops i mean $=2^n-1=65535$

3. 3psilon

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

4. satellite73

yes there are 16

5. satellite73

$2^n-1=65535$ $2^n=65526$ and $2^{16}=65536$

6. satellite73

another typo, $$2^n=65536$$

7. wio

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

Where $$a_0 = 1$$ and $$r=2$$...

9. nia_2012

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