<ol class="abc-list" start="2"><li><div class="list-item-content"><span class="list-item-text">A sequence ${{a}_{1}}$, ${{a}_{2}}$, ${{a}_{3}}$, … is given by</span></div><div class="list-item-paragraph" style="text-align: center">${{a}_{1}}=\frac{1}{2}$ and ${{a}_{n}}=\frac{{{n}^{2}}}{{{2}^{n}}}$ for $n\ge 1$.</div><div class="list-item-paragraph">Let ${{S}_{n}}$ be the sum of the first $n$ terms of the above sequence. Find the values of $p$ and $q$ such that ${{S}_{n}}=6-\frac{{{n}^{2}}+pn+q}{{{2}^{n}}}$ where $p$ and $q$ are constants.</div></li></ol>

A sequence ${{a}_{1}}$, ${{a}_{2}}$, ${{a}_{3}}$, … is given by

${{a}_{1}}=\frac{1}{2}$ and ${{a}_{n}}=\frac{{{n}^{2}}}{{{2}^{n}}}$ for $n\ge 1$.

Let ${{S}_{n}}$ be the sum of the first $n$ terms of the above sequence. Find the values of $p$ and $q$ such that ${{S}_{n}}=6-\frac{{{n}^{2}}+pn+q}{{{2}^{n}}}$ where $p$ and $q$ are constants.

Techniques of Differentiation - General

Techniques of Differentiation

H2 Math

International Baccalaureate Higher Level Mathematics

2023 HCI CT1 Q5 [Modified]

2023 HCI CT1 Q5 [Modified]

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