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Omni-MATH / Let a₁,a₂,⋯,a₄₁∈R, such that a₄₁=a₁,∑_(i=1)⁴⁰a_(i)=0, and for any i=1,2,⋯,40,|a_(i)−a_(i+1)|≤1. Determine the greatest possible value of (1)a₁₀+a₂₀+a₃₀+a₄₀; (2)a₁₀⋅a₂₀+a₃₀⋅a₄₀. · Discussion
Discussing Let a₁,a₂,⋯,a₄₁∈R, such that a₄₁=a₁,∑_(i=1)⁴⁰a_(i)=0, and for any i=1,2,⋯,40,|a_(i)−a_(i+1)|≤1. Determine the greatest possible value of (1)a₁₀+a₂₀+a₃₀+a₄₀; (2)a₁₀⋅a₂₀+a₃₀⋅a₄₀. · Omni-MATH
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