Please, describe the application of the Alternating Series Test for each series:

sibuzwaW 2021-08-20 Answered
Please, describe the application of the Alternating Series Test for each series:
a) \(\displaystyle{\sum_{{{n}={1}}}^{\infty}}\frac{{\left(-{1}\right)}^{{n}}}{{n}}\)
b) \(\displaystyle{\sum_{{{n}={1}}}^{\infty}}\frac{{1}}{{n}}\)
c) \(\displaystyle{\sum_{{{n}={1}}}^{\infty}}{\left(-{1}\right)}^{{n}}\)

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Expert Answer

Khribechy
Answered 2021-08-21 Author has 4505 answers
a) \(\displaystyle{\sum_{{{n}={1}}}^{\infty}}\frac{{\left(-{1}\right)}^{{n}}}{{n}}\) – the given series converges
b) \(\displaystyle{\sum_{{{n}={1}}}^{\infty}}\frac{{1}}{{n}}\) – the Alternatin Series Test is inconclusive or cannot be applied to the series
c) \(\displaystyle{\sum_{{{n}={1}}}^{\infty}}{\left(-{1}\right)}^{{n}}\) – the Alternatin Series Test is inconclusive or cannot be applied to the series
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