<ol class="abc-list"><li><div class="list-item-paragraph">The sum, \(S_n\), of the first \(n\) terms of a sequence \(u_1, u_2, u_3, \dots\) is given by \(S_n = 75 - \frac{3^{n+1}}{5^{n-2}}\).<br>Show that&nbsp;\(u_n = k\left(\frac{3}{5}\right)^{n-1}\), where&nbsp;\(k\) is a constant to be determined. Find \(S_\infty\).<span class="inline-marks">[4]</span></div></li><li><div class="list-item-paragraph">Another sequence of numbers \(v_1, v_2, v_3, \dots\) is such that&nbsp;\(\sum_{i=1}^{n} v_i = \frac{2n}{2n + 1}\).<br>Find the exact value of \(\sum_{i=11}^{\infty} v_i\).<span class="inline-marks">[3]</span></div></li></ol>

The sum, \(S_n\), of the first \(n\) terms of a sequence \(u_1, u_2, u_3, \dots\) is given by \(S_n = 75 - \frac{3^{n+1}}{5^{n-2}}\).
Show that \(u_n = k\left(\frac{3}{5}\right)^{n-1}\), where \(k\) is a constant to be determined. Find \(S_\infty\).

Another sequence of numbers \(v_1, v_2, v_3, \dots\) is such that \(\sum_{i=1}^{n} v_i = \frac{2n}{2n + 1}\).
Find the exact value of \(\sum_{i=11}^{\infty} v_i\).

2024 VJC Promo Q4

2024 VJC Promo Q4