MathDB

A sequence

a_0,a_1,a_2,\cdots

satisfies the conditions

a_0 = 0

a_{n-1}^2 - a_{n-1} = a_n^2 + a_n

1) determine the two possible values of

a_1

. then determine all possible values of

a_2

. 2)for each

n

, prove that

a_{n+1}=a_n+1

a_{n+1} = -a_n

3)Describe the possible values of

a_{1435}

4)Prove that the values that you got in (3) are correct

Problem Statement