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Worksheet 9.1—Sequences & Series: Convergence & Divergence Show all work. No calculator except unless specifically stated. Short Answer 1. Determine if the sequence 2 lnn n ½ ®¾ ¯¿ converges. 2. Find the nth term (rule of sequence) of each sequence, and use it to determine whether or not the sequence converges. (a) 2, 3 4, 4 9, 5 16, 6 ...
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Sequences and series. Determine the first 3 terms of the sequence tn = 2n - 6, nÎ{1, 2, 3, ...}. The first 3 terms are -4, -2, and 0. tn:{-0.9, -0.7, -0.5, ...} is an arithmetic sequence. - t = - 0 .5 - ( - 0 .7) = 0 . Thus, it is an arithmetic sequence. tn:{ , , , ...}. tn:{-10, -6, -2, ...}. The 10th term is 26.
Sequences. A sequence1 is a function whose domain is a set of consecutive natural numbers beginning with 1. For example, the following equation with domain {1, 2, 3, …} defines an infinite sequence2: a(n) = 5n − 3 or an = 5n − 3. The elements in the range of this function are called terms of the sequence.
In this section we define an infinite series and show how series are related to sequences. We also define what it means for a series to converge or diverge. We introduce one of the most important types of series: the geometric series.
ce are added, we obtain a series. Sequences and series are used to solve a variety of practical p. quence, arithmetic and geometric. This section will consider arithmetic sequences (also known as arithm. tic progressions, or simply A.P). The characteristic of such a sequence is that there is a common di. ference betw.
