<p>Evaluate \(\displaystyle\lim_{n\to\infty}\frac{1}{n}\sum_{k=1}^n\frac{1}{1+k/n}\) [JEE Main 2016]</p>
Step-by-Step Solution
Key Concept: Riemann sum \to \int_0^1 1/(1+x) dx = [ln(1+x)]_0^1 = ln 2.
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<p>$$\lim_{n\to\infty}\frac{1}{n}\sum_{k=1}^n\frac{1}{1+k/n}=\int_0^1\frac{dx}{1+x}=[\ln(1+x)]_0^1=\ln 2$$</p>
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Correct Answer: A