Question

Question #4380f

Answer 1

18446744073709551615

Explanation:

This can be represented as follows:

Amount for lets say the first 5 days:

1 + 2 + 4 + 8 + 16

We could represent this as:

`2^0 + 2^1 + 2^2 + 2^3 + 2^4`

And in summation notation:

`sum_(n = 0)^63(2^n)= 2^0+ 2^1+...+2^63= 18446744073709551615`

`n = 0` is first day.

`n = 63` is 64th day.

An alternative method is:

1 + 2 + 4 + 8 + 16 is a geometric series.

The common ratio is:

`2/1 = 4/2 = 2`

Using the formula for the sum of a geometric series:

`a((1 - r^n)/( 1 - r))`

Where `a` is the first term `r` is the common ratio and `n` is the last term.

`1((1 - 2^64)/(1 - 2)) = 18446744073709551615`