<ol class="abc-list"><li data-list-item-id="item-1759486577311-f3p3ywbtg"><ol class="i-list"><li data-list-item-id="subitem-1759486579621-1no5494nd"><div class="list-item-paragraph">Express $\frac{2{{r}^{2}}+1}{{{r}^{2}}-1}$. in the form $A+\frac{B}{r-1}+\frac{C}{r+1}$, where&nbsp;$A$, $B$ and $C$ are constants to be found.<span class="inline-marks">[2]</span></div></li><li data-list-item-id="subitem-1759486579780-pvu79j4x6"><div class="list-item-paragraph">Hence find $\sum\limits_{r=2}^{n}{\frac{2{{r}^{2}}+1}{{{r}^{2}}-1}}$ in terms of $n$.<span class="inline-marks">[4]</span></div></li></ol></li><li data-list-item-id="item-1759486584459-coro1yd6o"><div class="list-item-paragraph">Express $\sum\limits_{r=1}^{2n}{\left[ {{\left( -1 \right)}^{r+1}}{{2}^{r}} \right]}$ in the form $\frac{p}{q}\left[ s\left( {{4}^{n}} \right)+t \right]$, where&nbsp;$p$, $q$, $s$ and $t$ are integers to be determined.<span class="inline-marks">[3]</span></div></li></ol>

Express $\frac{2{{r}^{2}}+1}{{{r}^{2}}-1}$. in the form $A+\frac{B}{r-1}+\frac{C}{r+1}$, where $A$, $B$ and $C$ are constants to be found.

Hence find $\sum\limits_{r=2}^{n}{\frac{2{{r}^{2}}+1}{{{r}^{2}}-1}}$ in terms of $n$.

Express $\sum\limits_{r=1}^{2n}{\left[ {{\left( -1 \right)}^{r+1}}{{2}^{r}} \right]}$ in the form $\frac{p}{q}\left[ s\left( {{4}^{n}} \right)+t \right]$, where $p$, $q$, $s$ and $t$ are integers to be determined.

2021 CJC Promo Q5

2021 CJC Promo Q5

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