Sequences and Series

Lists of numbers that follow a rule, and what happens when you add them up — DfE content area D. Arithmetic and geometric series give exact formulae for sums, and the binomial expansion is extended to any rational power.

• An Overview — the two families of sequence, sigma notation, the key formulae and the common mistakes

The content statements

• Sequences and Sigma Notation — nth terms, recurrence relations, increasing, decreasing and periodic sequences, and Σ notation
• Arithmetic Sequences and Series — the nth term, the sum formula and its proof, and problems in context
• Geometric Sequences and Series — the nth term, the sum formula, the sum to infinity and modelling with logarithms
• The General Binomial Expansion — (a + bx)ⁿ for rational n, validity, approximations and partial fractions

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Each page has step-by-step notes, several worked examples, a quick-reference grid and ten practice questions with fully worked solutions.