An Alternating series is in the form: ∑(−1)nbn
Where bn≥0 An alternating series is not limited to these two forms because the exponent on the (-1) can vary.
The Alternating Series Test states that if the two following conditions are met, then the alternating series is convergent:
1. limn →∞bn=0
2. The sequence bn is a decreasing sequence.
For the second condition, bn does not have to be strictly decreasing for all n≥1. As long as the sequence is decreasing for n→∞, then that will be sufficient enough.
Convergence of the Alternating Series Test
Show that the following series converge:
Alternating series test
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