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Given the series    has infinite terms, what sum will this series approach but never reach? (type number only in box)

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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

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The infinite series \[1-1/2+1/2-1/3+1/3-\ldots\] converges. What is its sum?

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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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