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In a standard elimination tournament, a player wins $\$100k$ when she/he wins a match in the $k$th round. Develop and solve a recurrence relation for $a_n$, the total amount of money given away in a tournament with $n$ entrants, where $n$ is assumed to be a power of $2$.

I seem always to fail build recurrence relations... I hope someone could explain it to me in details.

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    I presume that $n$ is a power of $2$, not $2n$, and edited the question suitably.2011-11-16

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