Series (AQA A-Level Further Maths): Quizzes

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Summing Series Using Partial Fractions
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When does the method of differences work for summing a series?

When term written as f(r+1)f(r)f(r+1) - f(r)

What must be checked before attempting partial fraction decomposition?

Numerator degree < denominator degree

In the substitution method, which values should you choose to find constants?

Values that make factors equal to zero

What is a telescoping series?

Series where middle terms cancel

If partial fractions have factors rr and r+2r+2, which terms cancel?

Terms two rows apart

Why should differences be written vertically in method of differences?

To clearly see cancellation pattern

For infinite series, what must be shown after cancellation?

Remaining terms approach 0 as nn→∞

What is the standard form for partial fractions with two linear factors?

A(xa)+B(xb)\frac{A}{(x-a)} + \frac{B}{(x-b)}

After telescoping cancellation, which terms typically survive?

First few and last few terms only

What is a common mistake when setting up partial fractions?

Forgetting to multiply by denominator

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