Rearrangement of series. The theorem of Levy-Steiniz. - José Bonet ...
Rearrangement of series. The theorem of Levy-Steiniz. - José Bonet ...
Rearrangement of series. The theorem of Levy-Steiniz. - José Bonet ...
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<strong>The</strong> alternate harmonic <strong>series</strong>.<br />
<strong>The</strong> rearrangement <strong>of</strong> Laurent.<br />
1 − 1 1 1 1 1 1 1 1<br />
− + − − + − − ... =<br />
2 4 3 6 8 5 10 12<br />
= (1 − 1 1<br />
) − + (1<br />
2 4 3<br />
1 1 1 1<br />
− ) − + (1 − ) − ... =<br />
6 8 5 10 12<br />
= 1 1 1 1 1 1<br />
− + − + − ... =<br />
2 4 6 8 10 12<br />
= 1 1 1 1 1<br />
(1 − + − + ...) = log 2.<br />
2 2 3 4 2<br />
<strong>José</strong> <strong>Bonet</strong> <strong>Rearrangement</strong> <strong>of</strong> <strong>series</strong>. <strong>The</strong> <strong>theorem</strong> <strong>of</strong> <strong>Levy</strong>-<strong>Steiniz</strong>.
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