Sequences & Series
Mathematical Induction
Grade 11
Question:
<p>If <span class="math">P(n)</span> is a statement such that <span class="math">P(3)</span> is true. Assuming <span class="math">P(k) \text{ is true } \Rightarrow P(k+1) \text{ is true for all } k \geq 3</span>, then <span class="math">P(n)</span> is true</p>
<p>(a) for all n</p>
<p>(b) for all n ≥ 3</p>
<p>(c) for all n ≥ 1</p>
<p>(d) None of these</p>
Step-by-Step Solution
Key Concept: In mathematical induction, the statement is true for all natural numbers starting from the base case
<p><strong>Solution:</strong> By the principle of mathematical induction, if the base case holds at n=3 and the inductive step is true for all k≥3, then the statement P(n) is true for all n≥3.</p>
Correct Answer: B