"L'alphabet du millénaire"

Algebra Level 3

\[ \begin{eqnarray} A&=&2000\\ \\ B&=&A-999\\ \\ C&=&A+B-998\\ \\ D&=&A+B+C-997\\ & \vdots & \\ Z&=&A+B+C+...+Y-975 \end{eqnarray} \]

How much is \( \frac { Z+1 }{ { 2 }^{ 25 } } ? \)

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