Limits, Continuity & Differentiability
General
Grade 12
Question:
<p>For n ∈N, let an = Pn
k=1 2k and bn = Pn
k=1(2k −1). Then limn→∞(√an −√bn) is:</p>
Step-by-Step Solution
Key Concept: General
<p><strong>1</strong>: an = 2 \cdot n(n+1)</p> 2 = n2 + n.<p><strong>2</strong>: bn = n2 (Sum of first n odd numbers).</p><p><strong>3</strong>: Limit = \lim_{n \to \infty(</p>} \sqrt n2 + n -n) = \lim_{n \to \infty} n \sqrt n2+n+n = 1 1+1 = 1/2.
Correct Answer: 2