题目
数值题
Given the series has infinite terms, what sum will this series approach but never reach? (type number only in box)
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标准答案
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思路分析
The question as provided is missing the actual series expression (the part after 'Given the series' is blank). Without the specific terms, we cannot explicitly compute the sum that the infinite series approaches.
However, I can outline how you would determine such a sum in typical cases, and how the given answer (12) would be checked if the series were of a s......Login to view full explanation登录即可查看完整答案
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The infinite series \[1-1/2+1/2-1/3+1/3-\ldots\] converges. What is its sum?
Question text(1) Here is a convergent infinite series 1+1/2+1/4+1/8+1/16+...What kind of infinite series are we dealing with?Answer 1 Question 16[select: , arithmetic, geometric, p-series, harmonic, telescoping, none of the above]What is the fifth partial sum of this series (written in lowest terms)? Answer 2 Question 16[input] What's its sum? Answer 3 Question 16[input] (2). Here is another convergent infinite series 1+1/4+1/9+1/16+1/25+... What kind of infinite series are we dealing with?Answer 4 Question 16[select: , arithmetic, geometric, p-series, harmonic, telescoping, none of the above]What is the third partial sum of this series? Answer 5 Question 16[input] What is the integer part of its sum? Answer 6 Question 16[input] (3) Here is yet another converging infinite series What kind of infinite series are we dealing with?Answer 7 Question 16[select: , arithmetic, geometric, p-series, harmonic, telescoping, none of the above]What is the sum of the first three terms of this series? Answer 8 Question 16[input] What's its sum? Answer 9 Question 16[input] Check Question 16
Consider the series ∑ 𝑛 = 1 ∞ 0.01 . The terms are 𝑎 𝑛 = 0.01 . a) Find the following partial sums: 𝑆 1 = [ Select ] 0.01 0.02 1 0 0.03 𝑆 2 = [ Select ] 0.02 0.04 2 1 0.01 𝑆 3 = [ Select ] 3 4 0.03 0 0.01 𝑆 4 = [ Select ] 0.4 0.04 4 1 0.01 b) Find the limits: lim 𝑘 → ∞ 𝑆 𝑘 = [ Select ] infinity 0.04 0.01 negative infinity 0 and lim 𝑛 → ∞ 𝑎 𝑛 = [ Select ] negative infinity infinity 0.01 1 0 c) Does the series ∑ 𝑛 = 1 ∞ 0.01 converge or diverge? [ Select ] The series converges There is not enough information to tell The series diverges d) Suppose another series ∑ 𝑛 = 1 ∞ 𝑏 𝑛 has some unknown terms 𝑏 𝑛 but we know that lim 𝑛 → ∞ 𝑏 𝑛 = 0.01 (this means the numbers 𝑏 𝑛 are close to 0.01, but not necessarily equal to 0.01.) What can be said about the convergence of the series ∑ 𝑛 = 1 ∞ 𝑏 𝑛 ? [ Select ] The series converges The series diverges There is not enough information to tell
Consider the series ∑ 𝑛 = 1 ∞ 0.01 . The terms are 𝑎 𝑛 = 0.01 . a) Find the following partial sums: 𝑆 1 = [ Select ] 1 0.03 0.02 0.01 0 𝑆 2 = 0.02 𝑆 3 = [ Select ] 0.03 4 0.01 0 3 𝑆 4 = [ Select ] 0.4 0.01 0.04 4 1 b) Find the limits: lim 𝑘 → ∞ 𝑆 𝑘 = [ Select ] negative infinity 0 infinity 0.01 0.04 and lim 𝑛 → ∞ 𝑎 𝑛 = [ Select ] 1 infinity 0.01 negative infinity 0 c) Does the series ∑ 𝑛 = 1 ∞ 0.01 converge or diverge? The series diverges d) Suppose another series ∑ 𝑛 = 1 ∞ 𝑏 𝑛 has some unknown terms 𝑏 𝑛 but we know that lim 𝑛 → ∞ 𝑏 𝑛 = 0.01 (this means the numbers 𝑏 𝑛 are close to 0.01, but not necessarily equal to 0.01.) What can be said about the convergence of the series ∑ 𝑛 = 1 ∞ 𝑏 𝑛 ? The series diverges
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