Sequences, Series and Approximations
Behaviour in the long run, expansions, and numerical methods for roots.
01SequencesSequences defined by a formula or a recurrence relation, arithmetic and geometric sequences, what convergence and divergence mean, finding the limit of a sequence, and proving a formula by induction.100 questions02SeriesSigma notation, the sums of arithmetic and geometric series, the sum to infinity and when it exists, the standard results for sums of powers, and the method of differences.100 questions03The Binomial TheoremPascal's triangle and combinations, expanding a bracket raised to a positive integer power, the general term and how to pick out a single coefficient, the expansion for rational powers, and using it to approximate.100 questions04Roots of EquationsLocating a root by a sign change, narrowing it by interval bisection and linear interpolation, the Newton–Raphson method, fixed-point iteration and when it converges, and the ways these methods fail.100 questions