Talk:Geometric series: Difference between revisions
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imported>Peter Schmitt (→Convergence - misleading?: may be misunderstood, but was meant correctly) |
imported>Peter Schmitt m (→Convergence - misleading?: x, not q) |
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"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) | "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) | ||
: Thanks for the pointer. I have just started to edit this page and intend to make a few changes. You are right that it may be misleading, however, it obviously was meant to explain why the limit of the sum tends to a/(1- | : Thanks for the pointer. I have just started to edit this page and intend to make a few changes. You are right that it may be misleading, however, it obviously was meant to explain why the limit of the sum tends to a/(1-x). --[[User:Peter Schmitt|Peter Schmitt]] 23:16, 9 January 2010 (UTC) | ||
Revision as of 17:17, 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)
- Thanks for the pointer. I have just started to edit this page and intend to make a few changes. You are right that it may be misleading, however, it obviously was meant to explain why the limit of the sum tends to a/(1-x). --Peter Schmitt 23:16, 9 January 2010 (UTC)