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Start by alternately adding and subtracting fractions obtained by taking the reciprocal of odd numbers. This results in a series that is equivalent to pi divided by four. By rearranging the terms, a different infinite series is formed, in which positive terms are followed by negative terms in a specific pattern. Surprisingly, this rearranged series is also equal to pi divided by four. It seems counterintuitive, but the terms are the same as in the original series.
