Where's Eight?

Calculus Level 2

\[ \left ( 1 + \frac {1}{\color{purple}{2}} \right ) \left ( 1 + \frac {1}{\color{purple}{4}} \right ) \left ( 1 + \frac {1}{\color{purple}{16}} \right ) \dots = \ \color{teal} ? \]

Details and Assumptions:

  • \( \left (1 + \frac 1 8 \right ) \) is in fact not being multiplied.
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