Talk:Geometric series: Difference between revisions
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imported>Paul Wormer (New page: {{subpages}}) |
imported>Boris Tsirelson (→Convergence - misleading?: new section) |
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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). [[User:Boris Tsirelson|Boris Tsirelson]] 22:20, 9 January 2010 (UTC) | |||
Revision as of 17:20, 9 January 2010
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)