alleryEvaluate $\displaystyle\lim_{n\to\infty} \sum_{r=1}^{n} \dfrac{1}{n + r}$
A$0$
B$\ln 2$
C$\ln(1/2)$
D$1$
Answer & Solution
Correct answer: B. $\ln 2$
**Rewrite:** $\sum (1/n)\cdot 1/(1 + r/n) \to \int_0^1 dx/(1+x) = \ln(1+x)|_0^1 = \ln 2$.
(Riemann sum recognition.)
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