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### 11.2.misc1-eg-1

Course: MTH 132, Fall 2011
School: Michigan State University
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the Example 5 . 12n Is sequence {an } convergent or divergent? If it is convergent, nd its limit. Let an = Is the series an convergent or divergent? If it is convergent, nd its sum. n=1 1. Determine the limit of the sequence. 5 1 = 5 lim n n 12 n 12 The sequence converges and its limit is 0. lim n = 0 5 = 0. 2. Determine convegence of the series. By part a), the nth term test (for divergence) is...

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the Example 5 . 12n Is sequence {an } convergent or divergent? If it is convergent, nd its limit. Let an = Is the series an convergent or divergent? If it is convergent, nd its sum. n=1 1. Determine the limit of the sequence. 5 1 = 5 lim n n 12 n 12 The sequence converges and its limit is 0. lim n = 0 5 = 0. 2. Determine convegence of the series. By part a), the nth term test (for divergence) is inconclusive. However, the series 5 1 =5 n n=1 12 n=0 12 is a geometric series with r = 1 12 n+1 5 1 = 12 n=0 12 n which is convergent and its sum is given by 5 1 5 5 = =. n 12 1 (1/12) 11 n=1 12
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