<p>A sequence is defined by the recurrence relation</p>
<p style="text-align: center">${{u}_{n+1}}=\frac{1+{{u}_{n}}}{1-{{u}_{n}}}$,</p>
<p>for $n\ge 1$.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">State what happens to the sequence when ${{u}_{1}}=0$.</div><p style="text-align: right;">[1]</p></li></ol>
<p>It is now given that ${{u}_{1}}=2$.</p>
<ol class="abc-list" start="2"><li><div class="list-item-paragraph">Find ${{u}_{2}},\ {{u}_{3}},\ {{u}_{4}},\ {{u}_{5}}$ and ${{u}_{6}}$.</div><p style="text-align: right;">[2]</p></li><li><div class="list-item-paragraph">By observing the pattern in part <strong>(b)</strong>, find $\sum\limits_{r=1}^{4n}{{{u}_{r}}}$ in terms of $n$.</div><p style="text-align: right;">[2]</p></li></ol>

A sequence is defined by the recurrence relation

${{u}_{n+1}}=\frac{1+{{u}_{n}}}{1-{{u}_{n}}}$,

State what happens to the sequence when ${{u}_{1}}=0$.

Find ${{u}_{2}},\ {{u}_{3}},\ {{u}_{4}},\ {{u}_{5}}$ and ${{u}_{6}}$.

By observing the pattern in part **(b)**, find $\sum\limits_{r=1}^{4n}{{{u}_{r}}}$ in terms of $n$.

2024 HCI P1 Q2

2024 HCI P1 Q2

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