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Writing reciprocal of 2(m^2+m+1) as sum of consecutive terms

Source:

January 3, 2011

number theory unsolvednumber theory

Problem Statement

Show that the reciprocal of any number of the form

2(m^2+m+1)

, where

m

is a positive integer, can be represented as a sum of consecutive terms in the sequence

(a_j)_{j=1}^{\infty}

a_j = \frac{1}{j(j + 1)(j + 2)}