Riemann Sum – Exercise 2318

Exercise

Evaluate the limit

limnk=1n9k+3n3kn+2n2\lim_{n \rightarrow \infty}\sum_{k=1}^n \frac{9k+3n}{3kn+2n^2}

Final Answer


limnk=1n9k+3n3kn+2n2=3ln5+ln2\lim_{n \rightarrow \infty}\sum_{k=1}^n \frac{9k+3n}{3kn+2n^2}=3-\ln 5+\ln 2

Solution

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