Discussion 3A & 3B.docx

Discussion 3A & 3B.docx - Discussion 3A Explain what a...

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Discussion 3A Explain what a sequence is, what it means for a sequence to converge, and what techniques are available to us to determine if a sequence converges. Give an example of a sequence that converges or diverges and explain how this was determined. Sequence is the list of numbers written in a specific order. W hen a sequence converges , that means that as we get further along the sequence, the terms will get closer and closer to a specific limit (usually a real number). The techniques that can be used to determine if a sequences converges: 1. Evaluate the limit 2. Utilize sequence comparison theorems 3. Determine if the sequence is unbounded 4. Determine if the Sequence is Monotone and Bounded. 5. Apply the ratio test 6. Using subsequences For example: By using determine if the sequence is monotone and bounded. If we try to find some of the first number of the sequence by substituting n=5, n+1, n+2, and so on, we can know that this sequence is a decreasing sequence (and hence monotonic) since,
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