Limits, Continuity & Differentiability
Limits of Series
Grade 12
Question:
<p>The value of <span>\(\lim_{n \to \infty} \frac{1^3 + 2^3 + 3^3 + \ldots + n^3}{(n^2 + 1)^2}\)</span> is</p>
<p>(a) \(\frac{1}{4}\)</p>
<p>(b) \(\frac{1}{2}\)</p>
<p>(c) \(\frac{1}{2^2}\)</p>
<p>(d) None of these</p>
Step-by-Step Solution
Key Concept: Use the formula for sum of cubes: $\sum_{k=1}^{n} k^3 = \left[\frac{n(n+1)}{2}\right]^2$; then divide numerator and denominator by $n^4$.
<p>No solution provided in the page text.</p>
Correct Answer: A