Daily Archives: February 17, 2012

2012-2 sum with a permutation

Let n be a positive integer and let Sn be the set of all permutations on {1,2,…,n}. Assume \( x_1+x_2 +\cdots +x_n =0\) and \(\sum_{i\in A} x_i\neq 0 \) for all nonempty proper subsets A of {1,2,…,n}. Find all possible values of\[ \sum_{\pi \in S_n } \frac{1}{x_{\pi(1)}} \frac{1}{x_{\pi(1)}+x_{\pi(2)}}\cdots \frac{1}{x_{\pi(1)}+\cdots+ x_{\pi(n-1)}}. \]

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