If a series is finite, eg$\displaystyle \sum_{i=1}^\infty |x_i|^p < +\infty $ does that imply that since it is finite it is convergent....intuitively it seems correct...?

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- Oct 30th 2009, 03:30 AMbigdoggyFinite series
If a series is finite, eg$\displaystyle \sum_{i=1}^\infty |x_i|^p < +\infty $ does that imply that since it is finite it is convergent....intuitively it seems correct...?

- Oct 30th 2009, 04:38 AMKrizalid
well, more or less.

when we say "convergent," while summing terms, we'll see that the series tends to be a finite number.