This question was sent in by a student, which I think is rather interesting given 2015 A’levels P1 Q3 had something similar.

Use a definite integral to evaluate

\lim_{n \rightarrow \infty} \sum_{k=1}^{n} \frac{2n^2 + k^2}{n^3 + k^3},

given your answer correct to 5 decimal places.

Hint: Recall that the sum of area under the graph can be found using integration.

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