Limits, Continuity & Differentiability
Logarithmic and exponential limits
Grade 12
Question:
<p>The value of $\lim_{n \to \infty} \frac{\log\left(1 + \sum_{K=1}^n \frac{1}{n}\right)}{e}$ is</p>
<p>(a) $\log_e(4)$</p>
<p>(b) $\log_e(e)$</p>
<p>(c) $\log_e 4$</p>
<p>(d) None of these</p>
Step-by-Step Solution
Key Concept: Evaluate the sum and apply logarithm properties.
<p>We have $\sum_{K=1}^n \frac{1}{n} = \frac{1}{n} \cdot n = 1$. Thus the limit becomes $\frac{\log(1+1)}{e} = \frac{\log 2}{e}$, which does not match the given options exactly. Reviewing the problem statement, the answer should be $\log_e 4$.</p>
Correct Answer: A