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Infinite Geometric Series. An infinite series that is geometric. An infinite geometric series converges if its common ratio r satisfies –1 < r < 1. Otherwise it diverges. See also. Series, infinite, finite, geometric sequence

The infinite series had originated in India by the 14th c. An explicit formula for the sum of an infinite (anantya) geometric series is given by the 15th-16th c. Nilkantha in his Aryabhatyabhasya.(Sastri 1970, commentary on Ganita 17, p. 142.)

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This Geometric Sequence Calculator is used to calculate the nth term and the sum of the first n terms of a geometric sequence. If you like Geometric Sequence Calculator, please consider adding a link to this tool by copy/paste the following code

Free Geometric Sequences calculator - Find indices Equations Inequalities System of Equations System of Inequalities Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions Sequences Power Sums Induction Logical geometric sequence. What I want to Find.

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Answer to Use the formula for the nth partial sum of a geometric seriesSphereflakeThe sphereflake shown below is a....

edness of its partial sums is enough to ensure convergence. Theorem Boundedness Condition Suppose a n ≥0. Then P∞ n=1 a n converges if and only if the sequence of partial sums ( s n) = P n j=1 a j is bounded. Proof. The sequence (P n k=1 a k) is increasing. We saw in Section 6.3 that the sequence either converges, or it diverges to ...