Find the sum of the following series: 12+14−18+116+132−164+1128+1256−1512+⋯\frac12+\frac14-\frac18+\frac1{16}+\frac1{32} - \frac1{64} + \frac1{128} + \frac1{256} - \frac1{512} + \cdots

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