Number Theory

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What is $\log \prod_{n = 1}^{\infty} e^{2^{-n}}$?

NUMTH-WMSQHZ

What is $\log \prod_{n = 1}^{\infty} e^{2^{-n}}$?

A

$0$

B

$1$

C

$\infty$

D

$-\infty$