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A geometric series sums the terms of a geometric sequence, Sₙ = a(1 − rⁿ)/(1 − r), and converges to a sum to infinity a/(1 − r) when |r| < 1. This topic covers finite sums and sum to infinity. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive course teaches the method with worked examples and gives instant-feedback practice questions to lock it in.
How you do it
The sum of n terms is a times 1 minus r to the n, over 1 minus r. If the size of r is less than 1 the series converges, and the sum to infinity is a over 1 minus r. Check convergence before using that formula.
Before you start
Start once you are confident with geometric sequences. Pure 2 is where it is assessed. It underpins sum to infinity and convergence.
What you learn
The course works through the sum of n terms, the sum to infinity, sum to infinity with a term → a quadratic, forming and solving simultaneous equations and application: growth, decay and totals. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Geometric Series is part of the Sequences & Series strand of our free A-level maths courses, studied in the AS year. You work through 5 concepts and 5 worked examples, testing yourself at 5 points. Related topics students usually take next include Recurrence Relations, Arithmetic Sequences, Arithmetic Series, Binomial Expansion (C12) and Binomial Expansion (C34). The Sequences & Series revision engine gives you as many extra questions as you want, tracked on your skill tree.
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