Summing Series Using Partial Fractions (AQA A-Level Further Maths): Flashcards
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Technique when general term is
Technique when general term is
Method of differences
Key principle for method of differences
Key principle for method of differences
General term expressed as
Purpose of partial fractions in method of differences
Purpose of partial fractions in method of differences
Express term as difference of simpler fractions
Degree requirement before partial fraction decomposition
Degree requirement before partial fraction decomposition
Numerator degree < denominator degree
Method: substitute values making factors zero
Method: substitute values making factors zero
Substitution method
Series where intermediate terms cancel out
Series where intermediate terms cancel out
Telescoping series
Cancellation pattern for factors and
Cancellation pattern for factors and
Terms two rows apart cancel
How to arrange terms to see cancellation pattern
How to arrange terms to see cancellation pattern
Write terms vertically
Process for infinite series after cancellation
Process for infinite series after cancellation
Take limit as , remaining terms approach 0
Cancellation pattern for factors and
Cancellation pattern for factors and
Adjacent terms cancel