MathDB

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Part of 2006 Costa Rica - Final Round

Problems(2)

Find SUM 1/(i_1 i_2 ... i_r)

Source:

4/12/2006
Consider the set S={1,2,...,n}S=\{1,2,...,n\}. For every k∈Sk\in S, define Sk={X⊆S, k∉X,X≠∅}S_{k}=\{X \subseteq S, \ k \notin X, X\neq \emptyset\}. Determine the value of the sum Sk∗=∑{i1,i2,...,ir}∈Sk1i1⋅i2⋅...⋅irS_{k}^{*}=\sum_{\{i_{1},i_{2},...,i_{r}\}\in S_{k}}\frac{1}{i_{1}\cdot i_{2}\cdot...\cdot i_{r}} in fact, this problem was taken from an austrian-polish
algebra proposedalgebra
A functional relation. - compute f(2004).

Source: Costarrican Math Olympiad 2006 - Problem 4.

5/20/2006
Let ff be a function that satisfies : f(x)+2f(x+20012x−1)=4014−x. \displaystyle f(x)+2f\left(\frac{x+\frac{2001}2}{x-1}\right) = 4014-x. Find f(2004)f(2004).
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