Assume as known the (true) fact that the alternating harmonic series

(1)

is convergent, and denote its sum by s. Rearrange the series (1) as follows:

(2)

Assume as known the (true) fact that the series (2) is also convergent, and denote its sum by S. Denote by S_k, S_k the kth partial sum of the series (1) and (2), respectively. Prove the following statements.

(i)

(ii) S ≠ s

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