Sigma notation: changing the index

<ol class="i-list"><li><div class="list-item-paragraph">Express $\frac{3}{r}+\frac{2}{r+1}-\frac{5}{r+2}$ as a single fraction.<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">Hence find $\sum\limits_{r=1}^{n}{\frac{4r+3}{r\left( r+1 \right)\left( r+2 \right)}}$.<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">Use your answer to part (ii) to find $\sum\limits_{r=3}^{n}{\frac{4r-5}{r\left( r-1 \right)\left( r-2 \right)}}$.<span class="inline-marks">[2]</span></div></li></ol>

Express $\frac{3}{r}+\frac{2}{r+1}-\frac{5}{r+2}$ as a single fraction.

Hence find $\sum\limits_{r=1}^{n}{\frac{4r+3}{r\left( r+1 \right)\left( r+2 \right)}}$.

Use your answer to part (ii) to find $\sum\limits_{r=3}^{n}{\frac{4r-5}{r\left( r-1 \right)\left( r-2 \right)}}$.

Sigma Notation By Substitution

Sequence and Series

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

2022 TMJC P1 Q1

2022 TMJC P1 Q1

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