MathDB
u_{n + 2} = u_{n + 1} ++u_ n + [(-1)^n-1]/ 2}

Source: Mathley 2014 .1 p5

August 20, 2020
Sequencerecurrence relationalgebra

Problem Statement

Given the sequence (un)n=1∞(u_n)_{n=1}^{\infty}, where u1=1,u2=2u_1 = 1, u_2 = 2, and un+2=un+1+un+(−1)n−12u_{n + 2} = u_{n + 1} +u_ n+ \frac{(-1)^n-1}{2} for any positive integers nn. Prove that every positive integers can be expressed as the sum of some distinguished numbers of the sequence of numbers (un)n=1∞(u_n)_{n=1}^{\infty}
Nguyen Duy Thai Son, The University of Danang, Da Nang.
Back to ProblemsView on AoPS