Section10.2-SummingAnInfiniteSeries

N n 1 n otherwisetheseriesisdivergent

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Unformatted text preview: herwise, the series is divergent. (Thus, series have two associated sequences. These are the sequence of terms, {an}, and the sequence of partial sums, {sn}.) Geometric Series ar n 1 a ar ar 2 ar 3 ar n 1 n 1 Geometric series are distinguished by having a common ratio, r, of subsequent terms. Example: 1 3 4 n 1 n 1 2 3 1 1 1 1 3 3 3 3 3 4 4 4 4 n 1 Convergence of Geometric Series ar n 1 a ar ar 2 ar 3 ar n 1 n 1 For what values of r is the series convergent? sn a ar ar 2 ar 3 ar n 1 lim s n If r = 1, then sn= na. Clearly, , and series is divergent. n Now check other val...
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This note was uploaded on 02/24/2014 for the course APMA 1110 taught by Professor Morris during the Fall '11 term at UVA.

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