5.9 Alternating series test

Alternating series test

Lessons

Notes:
Note *An Alternating series is in the form:
(1)nbn\sum(-1)^nb_n
or
(1)n+1bn\sum(-1)^{n+1}b_n
Where bn0b^n \geq0 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. lim\limn →\infty bn=0b_n=0
2. The sequence bnb_n is a decreasing sequence.

For the second condition, bnb_n does not have to be strictly decreasing for all n1n\geq 1. As long as the sequence is decreasing for nn\infty, then that will be sufficient enough.
  • 2.
    Convergence of the Alternating Series Test
    Show that the following series converge:
Teacher pug

Alternating series test

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