MathDB

10

Part of 2001 Austrian-Polish Competition

Problems(1)

Maximize a sum

Source: Austrian-Polish 2001

9/19/2006
The sequence a1,a2,⋯ ,a2010a_{1},a_{2},\cdots,a_{2010} has the following properties: (1) each sum of the 20 successive values of the sequence is nonnegative, (2) ∣aiai+1∣≤1|a_{i}a_{i+1}| \leq 1 for i=1,2,⋯ ,2009i=1,2,\cdots,2009. Determine the maximal value of the expression ∑i=12010ai\sum_{i=1}^{2010}a_{i}.
inequalities unsolvedinequalities