This alternating infinite series converges: 1 - 1/3 + 1/5 - 1/7 + ... = pi/4 (Leibniz series). The absolute series 1 + 1/3 + 1/5 + 1/7 + ... probably diverges, but can the sum be associated with a finite number like other divergent series?

I'm guessing probably not. It is the harmonic series minus half the harmonic series, leaving half the harmonic series. Half of infinity is probably still infinity.

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