11.2.misc1-eg-1 - By part a), the n th term test (for...

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Example Let a n = 5 12 n . Is the sequence { a n } convergent or divergent? If it is convergent, find its limit. Is the series X n =1 a n convergent or divergent? If it is convergent, find its sum. 1. Determine the limit of the sequence. lim n →∞ 5 12 n = 5 lim n →∞ ± 1 12 ² n = 5 · 0 = 0 . The sequence converges and its limit is 0. 2. Determine convegence of the series.
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Unformatted text preview: By part a), the n th term test (for divergence) is inconclusive. However, the series X n =1 5 12 n = 5 X n =0 1 12 n +1 = 5 12 X n =0 1 12 n is a geometric series with r = 1 12 which is convergent and its sum is given by X n =1 5 12 n = 5 12 1 1-(1 / 12) = 5 11 ....
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