MathDB

26

Part of 2005 Postal Coaching

Problems(1)

A summation

Source: Indian Postal Coaching 2005

10/27/2005
Let a1,a2,…ana_1,a_2,\ldots a_n be real numbers such that their sum is equal to zero. Find the value of ∑j=1n1aj(aj+aj+1)(aj+aj+1+aj+2)…(aj+…aj+n−2). \sum_{j=1}^{n} \frac{1}{a_j (a_j +a _{j+1}) (a_j + a_{j+1} + a_{j+2}) \ldots (a_j + \ldots a_{j+n-2})}. where the subscripts are taken modulo nn assuming none of the denominators is zero.
number theory unsolvednumber theory