<ol class="abc-list"><li><div class="list-item-paragraph">Given that&nbsp;\(\sum_{r=1}^{n} r^{2} = \frac{n}{6}(n+1)(2n+1)\), evaluate \(\sum_{r=-n}^{n} (r+1)(r+3)\) in terms of \(n\).<span class="inline-marks">[4]</span></div></li><li><div class="list-item-paragraph">Using standard series from the List of Formulae (MF27), find the range of values of \(x\) for which the series \(\sum_{r=1}^{\infty} \frac{(-1)^{r+1} x^{r}}{r 2^{r}}\) converges. State the sum to infinity in terms of \(x\).<span class="inline-marks">[3]</span></div></li></ol>

Given that \(\sum_{r=1}^{n} r^{2} = \frac{n}{6}(n+1)(2n+1)\), evaluate \(\sum_{r=-n}^{n} (r+1)(r+3)\) in terms of \(n\).

Using standard series from the List of Formulae (MF27), find the range of values of \(x\) for which the series \(\sum_{r=1}^{\infty} \frac{(-1)^{r+1} x^{r}}{r 2^{r}}\) converges. State the sum to infinity in terms of \(x\).

2024 DHS Promo Q3

2024 DHS Promo Q3