Please reason step by step, and put your final answer within \boxed{}.
Given that the sum of the first $n$ terms of a sequence $\{a_{n}\}$ is ${S_n}={2^n}-1$, then the sum of the first $n$ terms of the sequence $\left\{{\frac{1}{{{a_n}}}}\right\}$ is $T_{n}=\_\_\_\_\_\_$.
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