- #1
sedaw
- 62
- 0
thres two series An and Bn , Bn unite with An from some index.
need to prove that limAn_k = limBn_m
Bn_m and An_m are sub series .
TNX !
need to prove that limAn_k = limBn_m
Bn_m and An_m are sub series .
TNX !
Convergence in the context of a unite series refers to the behavior of the series as the number of terms increases. If the terms of the series approach a finite limit as the number of terms increases, then the series is said to converge. Otherwise, it is said to diverge.
To determine if a unite series converges or diverges, you can use various tests such as the ratio test, the root test, or the integral test. These tests analyze the behavior of the series and provide a conclusive answer on convergence or divergence.
No, a unite series can only converge to one value. This is because the limit of a series is defined as the limit of the sequence of partial sums, and a sequence can only have one limit.
Yes, there are special cases where a unite series may converge to multiple values. These cases include series with alternating signs or series with terms that decrease at a slower rate. In these cases, the series may converge to more than one value, known as a conditional convergence.
The rate of convergence is a measure of how fast the terms of a series approach the limit. A faster rate of convergence means the series approaches the limit quickly, while a slower rate of convergence means the series approaches the limit more slowly. In general, a series with a faster rate of convergence is considered to be more well-behaved and easier to work with.