Word Count : 158

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To solve the limit numerically: \[ \lim_{n\rightarrow\infty }\sum_{r=1}^{2n}\frac{n^2}{(2n+r)^3} \] We will break this into steps: 1. Rewrite the sum: \[ S_n = \sum_{r=1}^{2n}\frac{n^2}{(2n + r)^3} \] We want to evaluate the behavior of \( S_n \) as \( n _______ ___ _____ _____ __________ ______ _________ _______ ________ _____.
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