Ononot — Consider the recurrence an = \sum{i=1}^{k} ci a{n-i}. If the

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Recurrence Relationshard

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Consider the recurrence $a_n = \sum_{i=1}^{k} c_i a_{n-i}$ . If the characteristic equation has roots $r_1, r_2, \dots, r_k$ all with absolute value $|r_i| < 1$ , what can be concluded about the sequence?