Show that the series , where if n is odd and if n is even, is divergent. Why does the Alternating Series Test not apply?
(i) is divergent.
(ii) Give reasons as to why the Alternating Series Test doesn’t apply.
i) Use theorem to show is divergent.
ii) Alternating Series Test:
If the alternating series
i) for all
then the series is convergent otherwise the series is divergent.
2) Theorem :
If and are convergent series, then, so are the series (where is a constant),
and , and
where if is odd
and if is even.
If is even
By comparison with the p-series test for , the series converges
Suppose on contrary,
converges and converges
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