Mathematics

Mathematics

Problem

A new series is formed by taking two positive terms of the alternating harmonic series for every one negative term, in the order: 1+13−12+15+17−14+19+111−16+⋯1 + \dfrac{1}{3} - \dfrac{1}{2} + \dfrac{1}{5} + \dfrac{1}{7} - \dfrac{1}{4} + \dfrac{1}{9} + \dfrac{1}{11} - \dfrac{1}{6} + \cdots What happens to this rearranged series? a) It converges and still sums to ln⁡2\ln 2. b) It converges, but to a value greater than ln⁡2\ln 2. c) It diverges to +∞+\infty. d) It diverges by oscillating between two finite bounds.

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