# Calculus question...

**URL:** <https://boards.straightdope.com/t/calculus-question/57263>\
**Category:** Factual Questions\
**Created:** [March 8, 2001, 8:29pm UTC](https://boards.straightdope.com/t/calculus-question/57263 "2001-03-08T20:29:53Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![Superdude](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/superdude/32/13450_2.png) [@Superdude](https://boards.straightdope.com/u/Superdude)\
**Post date:** [March 8, 2001, 8:29pm UTC](https://boards.straightdope.com/t/calculus-question/57263/1 "2001-03-08T20:29:53Z")

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Math not being my strong point, can someone tell me if the following sequence is convergent or divergent?

1-(3/2)+(9/4)-(27/8)+…

Thanks!

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**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\
**Post date:** [March 8, 2001, 9:53pm UTC](https://boards.straightdope.com/t/calculus-question/57263/2 "2001-03-08T21:53:46Z")

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1. That’s really more of series than a sequence, and
2. It’s divergent.

What you have there is an example of a _geometric series_, which is something of the form:

1 + r + r[sup]2[/sup] + r[sup]3[/sup] + ···

In this case, r=-3/2. Geometric series converge (with a sum of 1/(1-r)) if |r| \< 1, and diverge otherwise.

Another simple test for series in general (known as the Divergence test) is that if the terms don’t go to 0, the series diverges. In this case, the terms don’t go to 0. Hope that helps!