Real analysis proof
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Let {a_n} and {b_n} be sequences in [-infinity,+infinity] and prove the following assertions:
1).
a).Lim sup (as n -> infinity) ( a_n + b_n) less than or equal to lim sup a_n + lim sup b_n ( as n foes to infinity).
b).Show by an example that strict inequality can hold.
Provided none of the sums is of the form infinity negative infinity
2). If a_n less than or equal b_n for all n, then
lim inf a_n less than or equal lim inf b_n as n goes to infinity
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Solution Summary
This is a proof regarding lim sup of sequences.
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Real Analysis lim sup and lim inf
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Let {a_n} and {b_n} be sequences in [-infinity,+infinity] and prove the following assertions:
1).
a).Lim sup (as n -> infinity) ( a_n + b_n) less than or equal to lim sup a_n + lim sup b_n ( as n foes to infinity).
b).Show by an example that strict ...
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- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"
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