Sequences and series
Build and connect the representations and methods in sequences and series.
More
Offline pages
Saved on this device only. Connect at least once every 30 days to confirm Premium. Sign-out or a change of account removes saved copies.
Find this activity in your course
Before you begin
Build and connect the representations and methods in sequences and series.
Learning goals
- Express and use the general term of a sequence
- Find finite sums and analyse convergence of series
Syllabus statements covered
- Include: finite and infinite sequences and series; sequence as y = f(n) for positive integer n; nth term u_n and sum S_n relationship; sequences defined by nth-term formula or u_(n+1) = f(u_n), including calculator or computer generation; sum and difference of two series; convergence and sum to infinity; nth term and finite sum of arithmetic and geometric series; condition for convergence and sum to infinity of an infinite geometric series.
- Include: finite and infinite sequences and series; sequence as y = f(n) for positive integer n; nth term u_n and sum S_n relationship; sequences defined by nth-term formula or u_(n+1) = f(u_n), including calculator or computer generation; sum and difference of two series; convergence and sum to infinity; nth term and finite sum of arithmetic and geometric series; condition for convergence and sum to infinity of an infinite geometric series.
Lessons
Work through them in order.
About lesson progress
Lesson marks record what you have studied. Checks show understanding separately. Guest marks come from this device.
- Arithmetic, geometric and partial sumsDerive term and sum rules, retain geometric-ratio conditions, and check the first index and integer thresholds.
- Recurrence and convergenceGenerate valid terms, prove affine limits through their errors, and distinguish sequence, series and numerical stopping claims.