# A convergent series

Posted by Mathoman, Friday 29 October 2010 at 23:39 - Riddles And Exercises

To find out for which the series converges, one can use the following inequality which is valid for all ,

This inequality is easily proved (for example with the help of a drawing) and implies thatBy letting *n* go to infinity we conclude that the series converges if and diverges to infinity if Having this in mind, the following question is natural.

**Exercise:**

Let be a convergent series. Is it true that the series converges too?

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