$\lim _{n\to \infty }\left[\frac{1}{n}+\frac{n}{(n+1{)}^{2}}+\frac{n}{(n+2{)}^{2}}+\ldots \ldots +\frac{n}{(2n-1{)}^{2}}\right]$ is equal to: [JEE Main 2021, 25 Feb (Shift 2)]

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\(\lim _{n\to \infty }\left[\frac{1}{n}+\frac{n}{(n+1{)}^{2}}+\frac{n}{(n+2{)}^{2}}+\ldots \ldots +\frac{n}{(2n-1{)}^{2}…

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