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The Perplexed Banker

Question

I have some difficulties solving this problem, I searches on the Internet the answer, this was solved by geometric progression, but I don't understand how that was concluded, any hints?

A man went into a bank with a thousand dollars, all in dollar bills, and ten bags. He said, "Place this money, please, in the bags in such a way that if I call and ask for a certain number of dollars you can hand me over one or more bags, giving me the exact amount called for without opening any of the bags." How was it to be done? We are, of course, only concerned with a single application, but he may ask for any exact number of dollars from one to one thousand.

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Spoiler

Place the following in the 10 bags:

\$1, \$2, \$4,  \$8, \$16, \$32, \$64, \$128, \$256, \$489.

Combination of the contents of these bags would give you the correct amount from \$1 to \$1000.

Edited by rocdocmac
typo

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