True/False: For each of the following statements, determine if the statement is true or false. Provide...

 

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True/False: For each of the following statements, determine if the statement is true or false. Provide the reason which justify your answer. (a) For any sequence (an), there must be some integer k such that the sequence is Ak -constant. (b) The sum 1 + 3 + 5 + 7 + ··· + 1001 has exactly 500 terms. (c) Suppose an = 4an-1 - 3an-2. Then the characteristic equation is x 2 - 4x + 3 = 0 (d) Suppose an = an-1 + 5 with a0 = 2 Then (an) is an arithmetic sequence. (e) If 4 is a root of the characteristic equation of a linear homogeneous recurrence relation, then c. 4 n is a solution for any real number c. True/False: For each of the following statements, determine if the statement is true or false. Provide the reason which justify your answer. (a) For any sequence (an), there must be some integer k such that the sequence is Ak -constant. (b) The sum 1 + 3 + 5 + 7 + ··· + 1001 has exactly 500 terms. (c) Suppose an = 4an-1 - 3an-2. Then the characteristic equation is x 2 - 4x + 3 = 0 (d) Suppose an = an-1 + 5 with a0 = 2 Then (an) is an arithmetic sequence. (e) If 4 is a root of the characteristic equation of a linear homogeneous recurrence relation, then c. 4 n is a solution for any real number c.