Prove the following by the principle of mathematical induction: \[ \frac{1}{2}+\frac{1}{4}+\frac...

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Prove the following by the principle of mathematical induction:
\[
\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\ldots+\frac{1}{2^{n}}=1-\frac{1}{2^{n}}
\]
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