Where's Eight?

Calculus Level 2

(1+12)(1+14)(1+116)= ? \left ( 1 + \frac {1}{\color{#69047E}{2}} \right ) \left ( 1 + \frac {1}{\color{#69047E}{4}} \right ) \left ( 1 + \frac {1}{\color{#69047E}{16}} \right ) \dots = \ \color{teal} ?

Details and Assumptions:

  • (1+18) \left (1 + \frac 1 8 \right ) is in fact not being multiplied.
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