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Core Pure: series and proof

Quick questions on Method of differences: telescoping sums, partial fractions and the sum to infinity - OCR A-Level Further Maths A

2short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is q1?
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Given 1r(r+1)=1r−1r+1\dfrac{1}{r(r+1)} = \dfrac{1}{r} - \dfrac{1}{r+1}, state the sum to infinity of ∑r=1∞1r(r+1)\displaystyle\sum_{r=1}^{\infty}\dfrac{1}{r(r+1)}. [2 marks]
What is q2?
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Write 1r−1r+1\dfrac{1}{r} - \dfrac{1}{r+1} as a single fraction. [1 mark]

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