Series (Edexcel A-Level Further Mathematics): Quizzes

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Method of Differences
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What is the main property the method of differences uses to simplify series?

Telescoping property

What technique is often used to break down the general term in the method of differences?

Partial fractions

What is 1r(r+1)\frac{1}{r(r+1)} equal to in partial fractions?

1r−1r+1\frac{1}{r} - \frac{1}{r+1}

What happens to intermediate terms in a telescoping series?

They cancel out

What is ∑r=1n1r(r+1)\sum_{r=1}^n \frac{1}{r(r+1)} equal to?

1−1n+11 - \frac{1}{n+1}

What is the partial fraction form of 1r(r+2)\frac{1}{r(r+2)}?

12(1r−1r+2)\frac{1}{2}(\frac{1}{r} - \frac{1}{r+2})

What is the general partial fraction form of 1r(r+k)\frac{1}{r(r+k)}?

1k(1r−1r+k)\frac{1}{k}(\frac{1}{r} - \frac{1}{r+k})

Which is a common mistake when using the method of differences?

Omitting non-cancelled terms at the end

What remains after telescoping in a series?

First and last non-cancelled terms

When should the method of differences NOT be used?

On a series that does not telescope

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