$\lim _{n\to \infty }\frac{3}{n}\left{4+{\left(2+\frac{1}{n}\right)}^{2}+{\left(2+\frac{2}{n}\right)}^{2}+\ldots +{\left(3-\frac{1}{n}\right)}^{2}\right}$ is equal to [JEE Main 2023, 30 Jan (Shift 2)]

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\(\lim _{n\to \infty }\frac{3}{n}\left{4+{\left(2+\frac{1}{n}\right)}^{2}+{\left(2+\frac{2}{n}\right)}^{2}+\ldots +{\lef…

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