Geometric series, eh?

Algebra Level 4

{i=1ui=3i=1ui2=3\large{ \begin{cases} { \displaystyle \sum_{i=1}^{\infty} u_i = 3 } \\ { \displaystyle \sum_{i=1}^{\infty} u_i^2 = 3 } \end{cases}}

Let unu_n be the nthn^{th} term of a geometric series satisfying the conditions above. Evaluate 1000u10\lfloor 1000 u_{10} \rfloor .

Try my set.
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