Talk:Geometric series

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Revision as of 17:20, 9 January 2010 by imported>Boris Tsirelson (→‎Convergence - misleading?: new section)
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 Definition:  A series associated with a geometric sequence, i.e., consecutive terms have a constant ratio. [d] [e]
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Convergence - misleading?

"converges when |x| < 1, because in that case xk tends to zero" — the reader may conclude that convergence to 0 of terms of a series implies convergence of the series (that is, of partial sums), which is of course false (harmonic series is the simplest counterexample). Boris Tsirelson 22:20, 9 January 2010 (UTC)

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