Adding up a pattern of terms exactly. The method of differences is the elegant one: write each term as a difference so nearly everything cancels.
Syllabus points covered
- Use the standard results for Σr, Σr² and Σr³
- Use the method of differences to obtain the sum of a finite series
- Recognise a telescoping series and identify which terms survive
- Find the sum to infinity of a convergent series where appropriate
Common mistakes
- Applying Σr from 1 to n when the series starts elsewhere. Subtract the earlier part.
- In the method of differences, not writing out enough terms to see which ones actually cancel.
- Forgetting that Σ of a constant over n terms is n times that constant, not the constant.
- Assuming a series converges without checking the remaining terms tend to zero.
Worksheets
Use these as soon as you've learned the topic and need to practise it. Start with the worksheet, check yourself against the answers, and only then look at the step-by-step solutions.
- Practice worksheet
- Worksheet answers
- Step-by-step solutionsComing soon
Topical past papers
Move on to these once you've worked through the worksheets and are ready for harder, exam-style questions. Real past-paper questions on this topic, with the official mark scheme and full worked solutions.
- Topical questions
- Mark scheme
- Step-by-step worked solutionsComing soon
Looking for whole papers by session? All Further Mathematics past papers