• jtesttubes
In summary, the conversation was about a question regarding the sum of money given over 30 days when starting with $1 and doubling it each day. The solution involves a geometric sum formula and results in a total of$1073741823.

#### 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.

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

Don't know what the number is.

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.

Last edited by a moderator:
THanks Halls of Ivory. I switched the base and exponent.

Couldn't you just do

$$30!=2.6525286\cdot10^{32}$$

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

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

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