SOLUTION: My uncle has 6 million dollars to spend. On the first day he spent $1, on the second day he spent $2, on the third day he spent $4, and so forth with the amount doubling every day

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Question 1028128: My uncle has 6 million dollars to spend.
On the first day he spent $1, on the second day he spent $2, on the third day he spent $4, and so forth with the amount doubling every day.
If he continues to spend every day, how long will his 6 million dollars last?
Answer by jorel555(1290) About Me  (Show Source):
You can put this solution on YOUR website!
Let's use the first 4 days. Your uncle will have spent:
1+2+4+8=15
15+1=16=2^4
Similarly, for five days we have:
1+2+4+8+16=31
31+1=32=2^5
Generalizing, it is apparent that the sum of 2^0+2^1+2^2+....+2^n=2^n+1
If we want to spend 6 million dollars, then:
2^n+1=6000000
2^n=5999999
n, in this case, is somewhere between 2^22 and 2^23, so his money will last only until shortly after the 22nd day!!!!!!!!!!!!!