<ol class="abc-list"><li data-list-item-id="imported-item-block-0-item-0" data-list-item-path="imported-item-block-0-item-0"><div class="list-item-paragraph">Show that&nbsp;\(\frac{1}{r(r+1)(r+2)} = \frac{A}{r} + \frac{B}{(r+1)} + \frac{C}{(r+2)}\), where&nbsp;\(A\), \(B\) and \(C\) are constants to be found.<span class="inline-marks">[2]</span></div></li><li data-list-item-id="imported-item-block-0-item-1" data-list-item-path="imported-item-block-0-item-1"><div class="list-item-paragraph">Hence find \(\sum_{r=1}^{n} \frac{1}{r(r+1)(r+2)}\).<span class="inline-marks">[3]</span></div></li><li data-list-item-id="imported-item-block-0-item-2" data-list-item-path="imported-item-block-0-item-2"><div class="list-item-paragraph">Give a reason why the series \(\sum_{r=2}^{\infty} \frac{1}{r(r+1)(r+2)}\) converges, and write down its value.<span class="inline-marks">[2]</span></div></li></ol>

Show that \(\frac{1}{r(r+1)(r+2)} = \frac{A}{r} + \frac{B}{(r+1)} + \frac{C}{(r+2)}\), where \(A\), \(B\) and \(C\) are constants to be found.

Hence find \(\sum_{r=1}^{n} \frac{1}{r(r+1)(r+2)}\).

Give a reason why the series \(\sum_{r=2}^{\infty} \frac{1}{r(r+1)(r+2)}\) converges, and write down its value.

2018 TGM P2 Q3 [Out of 2025 Syllabus]

2018 TGM P2 Q3 [Out of 2025 Syllabus]

Solution:

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