AP EAMCET · Maths · Limits
\(\lim _{n \rightarrow \infty} \frac{1}{n^3} \sum_{k=1}^n k^2 x=\)
- A x
- B \(\frac{x}{2}\)
- C \(\frac{x}{3}\)
- D \(\frac{x}{4}\)
Answer & Solution
Correct Answer
(C) \(\frac{x}{3}\)
Step-by-step Solution
Detailed explanation
\( \lim _{n \rightarrow \infty} \frac{x}{n^3} \frac{n(n+1)(2n+1)}{6} \) \( = \frac{x}{6} \lim _{n \rightarrow \infty} \frac{n(n+1)(2n+1)}{n^3} \) \( = \frac{x}{6} \lim _{n \rightarrow \infty} \frac{n^3(1+\frac{1}{n})(2+\frac{1}{n})}{n^3} \) \( = \frac{x}{6} (1)(2) \)…
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