Riemann Sum – Exercise 2322

Exercise

Evaluate the limit

limnk=1n(n+knn)2\lim_{n \rightarrow \infty}\sum_{k=1}^n {(\frac{n+k}{n\sqrt{n}})}^2

Final Answer


limnk=1n(n+knn)2=73\lim_{n \rightarrow \infty}\sum_{k=1}^n {(\frac{n+k}{n\sqrt{n}})}^2=\frac{7}{3}

Solution

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