CSE 215 Lecture 14: Induction and Sequences

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22 Mar 2017
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Sequence: 2, 5, 8, 11, 14, 17, . Sometimes specified by a formula of its generic term. Represents the sequence: 2, 4, 8, 16, 32, 64, 128, . Ak = k/(k+1), for all k >= 1: Bk = (i-1)/i, for all i >= 2: Consider the sequence: 1, -(1/4), (1/9), -(1/16), (1/25), -(1/36) Observe that the denominator of each term is a perfect square. M is the lower limit of the summation. N is the upper limit of the summation. A1 = -2, a2 = -1, a3 = 0, a4 = 1, a5 = 2. In the last summation, k is still going from 1 to 2, but this is doubled in the index since the index is listed as 2k. Summation i = 1 to 7 for function i2 = (1)2 + 22 + 32 + + 72. Summation i = 1 to 5 for function i+4 = (1+4) + (2+4) + + (7+4)

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