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An infinite product either converge towards 1, either diverge. So the answer is either a) or b).
We compose the expression by log to get a sum. We now study sum of log(1+delta^(2^k)). When k->+inf, this term is equivalent to delta^(2^k).
Sum of delta^(2^k) converges when n->+inf (geometric sum). Thus, by theorem of comparison, sum of log(1+delta^(2^k)) converges.
Thus, the product converges and converges towards 1. So answer A).
