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UPCET / UPSEE Riemann Limit — practice questions

Explore 1 free Riemann Limit questions in UPCET / UPSEE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Riemann Limit questions and exercises with answers

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Evaluate $\displaystyle\lim_{n\to\infty} \sum_{r=1}^{n} \dfrac{1}{n + r}$Read the answer and worked solution →

Worked practice questions

Evaluate $\displaystyle\lim_{n\to\infty} \sum_{r=1}^{n} \dfrac{1}{n + r}$

  1. $0$
  2. $\ln 2$
  3. $\ln(1/2)$
  4. $1$
Show answer and 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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