Section10.2-SummingAnInfiniteSeries

N nowcheckothervaluesofr convergenceofgeometricseries

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Unformatted text preview: ues of r… Convergence of Geometric Series ‐ continued sn a ar ar 2 ar 3 ar n 1 1 rsn ar ar 2 ar 3 ar n 1 ar n sn rsn a ar n 1 sn 1 r a 1 r n a sn 1 r n 1 r if r ≠ 1 2 1 2 1 Convergence of Geometric Series ‐ continued a sn 1 r n 1 r If r 1, then lim sn n if r ≠ 1 a 1 r If r 1, then lim sn . n If r 1, then lim sn does not exist. n Convergent Divergent Divergent Summary The geometric series, ar n 1 a ar ar 2 ar 3 ar n 1 n 1 r 1 is convergent if . Otherwise, the series is divergent. a 1 r If convergent, the sum is . Bug Example Conclusion n 1 1 1 d l l n 1...
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