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6

Part of 2003 Turkey Team Selection Test

Problems(1)

Non-decreasing integ seq. with sum of terms is equal to n

Source: Turkey TST 2003 - P6

4/6/2013
For all positive integers nn, let p(n)p(n) be the number of non-decreasing sequences of positive integers such that for each sequence, the sum of all terms of the sequence is equal to nn. Prove that 1+p(1)+p(2)+⋯+p(n−1)p(n)≤2n.\dfrac{1+p(1)+p(2) + \dots + p(n-1)}{p(n)} \leq \sqrt {2n}.
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