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 &minus;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

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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.