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Given is a sequence bn defined in recursive form 1 A * = (-+ ^^) bn - n-1 2 bn-1 for a given A> 0. You can assume that all values of bn are non-zero. (a) For A 2 use your calculator (or MATLAB) to calculate the first four values of the sequence bn starting from b₁ A (this is for n = 1, 2, 3, 4). Inspecting these values: do you expect the sequence to be convergent or to be divergent? = (b) Assume you know the sequence bn is converging, what would be its limit (or its limits)? Justify your answer. Is it consistent with your result of part (a)?

Given is a sequence bn defined in recursive form 1 A * = (-+ ^^) bn - n-1 2 bn-1 for a given A> 0. You can assume that all values of bn are non-zero. (a) For A 2 use your calculator (or MATLAB) to calculate the first four values of the sequence bn starting from b₁ A (this is for n = 1, 2, 3, 4). Inspecting these values: do you expect the sequence to be convergent or to be divergent? = (b) Assume you know the sequence bn is converging, what would be its limit (or its limits)? Justify your answer. Is it consistent with your result of part (a)?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Given is a sequence bn defined in recursive form bn 1/1 (02-1 + 04-1) A = bn-1 2 bn-1 for a given A > 0. You can assume that all values of bn are non-zero. (a) For A = 2 use your calculator (or MATLAB) to calculate the first four values of the sequence bn starting from b₁ A (this is for n = 1, 2, 3, 4). Inspecting these values: do you expect the sequence to be convergent or to be divergent? = (b) Assume you know the sequence bn is converging, what would be its limit (or its limits)? Justify your answer. Is it consistent with your result of part (a)?
Transcribed Image Text:Given is a sequence bn defined in recursive form bn 1/1 (02-1 + 04-1) A = bn-1 2 bn-1 for a given A > 0. You can assume that all values of bn are non-zero. (a) For A = 2 use your calculator (or MATLAB) to calculate the first four values of the sequence bn starting from b₁ A (this is for n = 1, 2, 3, 4). Inspecting these values: do you expect the sequence to be convergent or to be divergent? = (b) Assume you know the sequence bn is converging, what would be its limit (or its limits)? Justify your answer. Is it consistent with your result of part (a)?
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