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

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Prove the following by the principle of mathematical induction:

\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + + \frac{1}{2 ^{n}} = 1 - \frac{1}{2 ^{n}}

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Prove the following by the principle of mathematical induction:

\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + + \frac{1}{2 ^{n}} = 1 - \frac{1}{2 ^{n}}

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