Basic Mathematics & Logarithm
Mathematical Induction
Grade 11
Question:
<p>If <latex>a_n = \sqrt{7\sqrt{7\sqrt{7\cdots}}}</latex> having n radical signs, then by mathematical induction which one is true?</p>
<p>(a) <latex>a_n \geq 7, \forall n \geq 1</latex></p>
<p>(b) <latex>a_n \geq 3, \forall n \geq 1</latex></p>
<p>(c) <latex>a_n < 4, \forall n \geq 1</latex></p>
<p>(d) <latex>a_n < 3, \forall n \geq 1</latex></p>
Step-by-Step Solution
Key Concept: Use mathematical induction to find bounds on the nested radical sequence.
<p>To be determined from textbook solution.</p>
Correct Answer: c