THE DEFINITE INTEGRAL The limit \[ \lim _{n \rightarrow \infty} \sum_{k=1}^{n}\left(\frac{2}{n}+\frac{3 k}{n^{2}}\right)= \] can be written as a definite integral on the interval \( [0,2] \) as
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First, we can rewrite the sum as \[ \frac{2}{n}\sum_{k=1}^{n}1+\frac{3}{n^{2}}\sum_{k=1}^{n}k \] Show more…
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