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- #1

- Jan 26, 2012

- 4,055

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Remember to read the POTW submission guidelines to find out how to submit your answers!

- Thread starter Jameson
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- Thread starter
- Admin
- #1

- Jan 26, 2012

- 4,055

--------------------

Remember to read the POTW submission guidelines to find out how to submit your answers!

- Thread starter
- Admin
- #2

- Jan 26, 2012

- 4,055

1) dwsmith

2) veronica1999

3) Sudharaka

Solution (modified slightly from Sudharka):

\[S_n=2^0+2^1+2^2+\cdots+2^{n-1}=\frac{1-2^n}{1-2}=2^n - 1\]

Therefore the sum of the money taken after 30 days,

\[S_{30}=\frac{2^{30}-1}{100}=10,737,418.23>5,000,000\] (we divide by 100 because there are 100 pennies in 1 dollar)

So better to take the second option!

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