Suppose the sequence {an}∞n = 0 is defined by the recurrencerelation an + 1 = (1)/(3)an + 6; a0 = 3.a. Prove that the sequence is increasing and bounded.b. Explain why {an}∞n = 0 converges and find the limit.

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.