How Much Money Would You Have After 30 Days of Doubling?

[jtesttubes]

I have been asked this question before 6 months, it was an interesting question.

Here is the question i just want to share.
Today let me simplify it as 1st day i give 1 $ 2nd Day i double it to 2$ I am going to give you like this for 30 days how much money i would have totally given at the end of 30 days... this is the question initially i thought simple and i found there is really a calculation behind it. I leave it to the members to find out the answer.

 

[flatmaster]

Sum((n-1)^2,n=1,30)

Don't know what the number is.

 

[HallsofIvy]

No, "doubling" would be 2^{n-1}, not (n-1)^2.

And the sum: \sum_{n=1}^{30} 2^{n-1} is a geometric sum. A geometric sum is of the form \sum_{n=0}^N ar^{n-1}. It is well known that it totals
a\frac{1- r^{N}}{1- r}
For a= 1, r= 2, that is
\sum_{n=0}^N= \frac{1- 2^N}{1- 2}= 2^{N}- 1
For n= 30, that is 2³⁰-1= 1073741823.

 

[flatmaster]

THanks Halls of Ivory. I switched the base and exponent.

 

[davidblair]

Couldn't you just do

30!=2.6525286\cdot10^{32}

Edit: Never mind, I read the original question wrong.

 

[jtesttubes]

Ok david you have worked it out well, what is the answer in $