Let \( \mathrm{a}_{1}, \mathrm{a}_{2}, \ldots \ldots . . \mathrm{a}...

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Let \( \mathrm{a}_{1}, \mathrm{a}_{2}, \ldots \ldots . . \mathrm{a}_{n} \), be real numbers such that \( \sqrt{a_{1}}+\sqrt{a_{2}-1}+\sqrt{a_{3}-2}+\ldots \ldots+\sqrt{a_{n}-(n-1)}=\frac{1}{2}\left(a_{1}+a_{2}+\ldots \ldots+a_{n}\right)-\frac{n(n-3)}{4} \)
\( \mathrm{P} \) then find the value of \( \sum_{i=1}^{100} a_{i} \)
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