Geometric series: Difference between revisions
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A '''geometric series''' is a [[series (mathematics)|series]] associated with an infinite [[geometric sequence]], | |||
i.e., the quotient ''q'' of two consecutive terms is the same for each pair. | |||
A geometric series converges if and only if −1<''q''<1. | |||
A '''geometric series''' consisting of ''n'' terms is, | A '''geometric series''' consisting of ''n'' terms is, | ||
:<math> | :<math> |
Revision as of 13:07, 9 January 2010
A geometric series is a series associated with an infinite geometric sequence, i.e., the quotient q of two consecutive terms is the same for each pair.
A geometric series converges if and only if −1<q<1.
A geometric series consisting of n terms is,
where a and x are real numbers. It can be shown that
The infinite geometric series converges when |x| < 1, because in that case xk tends to zero for and hence
The geometric series diverges for |x| ≥ 1.