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jlu
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how can i can the convergence of sum[sin (0.4)n / n pi]2 and that sum[sin (0.4)n / n pi] diverges, n is between -infinity and + infinity
jlu said:how can i can the convergence of sum[sin (0.4)n / n pi]2 and that sum[sin (0.4)n / n pi] diverges, n is between -infinity and + infinity
Convergence in a sequence refers to the behavior of the terms in a sequence approaching a certain value as the number of terms increases. In other words, the terms in the sequence get closer and closer to a fixed value as more terms are added.
There are a few different tests that can be used to determine convergence in a sequence, such as the limit test, ratio test, and root test. These tests involve evaluating the limit of the sequence or comparing it to a known convergent or divergent sequence.
Absolute convergence refers to a sequence where the terms always approach a certain value, regardless of the order in which they are added. On the other hand, conditional convergence refers to a sequence where the terms only approach a certain value when they are added in a specific order.
No, a sequence can only converge to one value. If a sequence approaches more than one value, it is considered to be divergent.
If a sequence does not converge, it is considered to be divergent. This means that the terms in the sequence do not approach a fixed value, and the behavior of the terms may be unpredictable.