MATH 1005 Lecture Notes - Ibm System P, Direct Comparison Test
6 Feb 2014
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[3: the sum of the series (a) 3 (b) 1 n n (iii) n=1 (a) (i), (ii) and (iii) (cid:1) n (iii) n2 + 1 n=0 (a) (i), (ii) and (iii) Answer: (c) (b) (i) and (ii) (c) (ii) (d) (ii) and (iii) (e) (iii) (cid:1) n=1 n2 + 2n + 1 n4 + 1 converges. Solution: n2 + 2n + 1 lim n n4 + 1. = 1 (cid:3)= 0 the series diverges by the nth-term test. Justify your answer. is a divergent geometric series since r = and |r| 1. [3: determine whether or not the series (cid:2) (cid:3)n. [3: determine whether or not the series. 1 n2 and n3 + 3 converges by the comparison test. n=1. 1 n2 is a convergent p-series since p = 2 > 1. 2 x as a power series about (centred at) a = 1 for |x 1| < 1. 2(x 1)n for |x 1| < 1. n=0.
