<p>Example \(2\). A sequence \(\{u_n\}\) is defined by \(u_n = \frac{(-1)^n}{n}, n = 1, 2, 3, \dots\)</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Write down the first four terms of this sequence.</span></div></li></ol>
<ol class="i-list" start="2"><li><div class="list-item-content"><span class="list-item-text">Explain why \(-\frac{1}{144}\) is not a term of \(\{u_n\}\).</span></div></li></ol>
<p>(Hint: Use a proof by contradiction.)</p>
<ol class="i-list" start="3"><li><div class="list-item-content"><span class="list-item-text">Another sequence \(\{v_n\}\) is formed by taking the \(1^{\mathrm{st}}\), \(3^{\mathrm{rd}}\), \(5^{\mathrm{th}}\), and in general, all the odd-positioned terms of \(\{u_n\}\). Write, in terms of \(n\), an expression for&nbsp;\(\{v_n\}\).</span></div></li></ol>

Example \(2\). A sequence \(\{u_n\}\) is defined by \(u_n = \frac{(-1)^n}{n}, n = 1, 2, 3, \dots\)

Write down the first four terms of this sequence.

Explain why \(-\frac{1}{144}\) is not a term of \(\{u_n\}\).

Another sequence \(\{v_n\}\) is formed by taking the \(1^{\mathrm{st}}\), \(3^{\mathrm{rd}}\), \(5^{\mathrm{th}}\), and in general, all the odd-positioned terms of \(\{u_n\}\). Write, in terms of \(n\), an expression for \(\{v_n\}\).

APGP

International Baccalaureate Higher Level Mathematics

Terms of a sequence

Terms of a sequence