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Part of 2002 Putnam

Problems(2)

Putnam 2002 A3: average of the elements of a set is integer

Source: 0

11/2/2011
Let NN be an integer greater than 11 and let TnT_n be the number of non empty subsets SS of {1,2,.....,n}\{1,2,.....,n\} with the property that the average of the elements of SS is an integer.Prove that Tn−nT_n - n is always even.
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Putnam 2002 B3

Source:

3/12/2012
Show that for all integers n>1n>1, 12ne<1e−(1−1n)n<1ne. \dfrac {1}{2ne} < \dfrac {1}{e} - \left( 1 - \dfrac {1}{n} \right)^n < \dfrac {1}{ne}.
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