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Pure · Sequences & series

Chapter 1 · 4

The idea

Sigma notation and recurrence relations

Reading and evaluating sums written with Σ, and generating sequences from a recurrence relation — including spotting periodic behaviour.

A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.

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Pure · Sequences & series

Sigma notation and recurrence relations

Reading and evaluating sums written with Σ, and generating sequences from a recurrence relation — including spotting periodic behaviour.

Why it works

Two ways to describe a sequence

This lesson is about notation — two compact ways of writing things you can already do. Σ\Sigma compresses "add all of these up" into one symbol, and a recurrence relation compresses "each term comes from the one before" into one rule. Neither adds new maths; both appear on almost every paper, and misreading them is where the marks go.

Reading a sigma

∑r=1nf(r)\displaystyle\sum_{r=1}^{n} f(r) means: substitute r=1,2,…,nr = 1, 2, \dots, n into f(r)f(r) and total the results:

∑r=1nf(r)=f(1)+f(2)+⋯+f(n)\sum_{r=1}^{n} f(r) = f(1) + f(2) + \cdots + f(n)

Keep reading — free

The rest of the explanation, plus 3 worked examples you step through move by move.

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