MathDB
sum 1/{a_j(a_j+a_{j+1})(a_j+a_{j+1}+a_{j+2})...(a_j+a_{j+1}+...+a_{j+n-2})}}

Source: Oliforum Contest I 2008 unused https://artofproblemsolving.com/community/c2487525_oliforum_contes

September 28, 2021
algebra

Problem Statement

Let a1,a2,...,an a_1,a_2,...,a_n with arithmetic mean equals zero; what is the value of: ∑j=1n1aj(aj+aj+1)(aj+aj+1+aj+2)...(aj+aj+1+...+aj+n−2) \sum_{j=1}^n{\frac{1}{a_j(a_j+a_{j+1})(a_j+a_{j+1}+a_{j+2})...(a_j+a_{j+1}+...+a_{j+n-2})}} , where an+k=ak a_{n+k}=a_k ?
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