Abstract
Editorial comment. From f (a) = 2 , a(i)2 2 a (i)a(i + 1), it follows that the largest value of Ua(i)at(i + 1) is I3n1I i2 (2n 3) = (2n3 + 3n2 _ 11n + 18)/6. This is problem B-3 from the 1996 William Lowell Putnam Mathematical Competition (this MONTHLY 104 (1997) 744-754). John H. Lindsey II and Ricardo Garcia-Pelayo mentioned that the examples in (1) and (2) are also extremal for a large class of sums of the form iZ=I h(a (i) a (i + 1)), where h is even, nonnegative, and convex.
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