MHT CET · Maths · Limits
The value of \(\lim _{x \rightarrow \infty} \frac{1+2+3 \ldots+n}{n^{2}}\) is
- A 1
- B \(\frac{1}{2}\)
- C 0
- D \(\frac{3}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(\lim _{n \rightarrow \infty} \frac{1+2+3+\ldots+n}{n^{2}}=\lim _{n \rightarrow \infty} \frac{n(n+1)}{2 n^{2}}\)
\(=\lim _{n \rightarrow \infty} \frac{\left(1+\frac{1}{n}\right)}{2}=\frac{1}{2}\)
\(=\lim _{n \rightarrow \infty} \frac{\left(1+\frac{1}{n}\right)}{2}=\frac{1}{2}\)
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