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Algebra Level 4

If Sn=r=1ntr=2n3+9n2+13n6S_n=\displaystyle\sum_{r=1}^{n} t_{r} = \dfrac{2n^3+9n^2+13n}{6} for all positive integers nn, evaluate r=110tr\displaystyle\sum_{r=1}^{10} \sqrt{t_r} .

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