find a limit of polynom

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What is the limit of P(n) = (1+1/2)(1+1/2^2)...(1+1/2^n) when n -> +Infinity? I calculated on my computer this function and for large number its value converges to 2.3842310290313713. I am curious whether can this polynom be simpified or can we somehow express the limit in logarithms or other mathematical functions.