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  1. G

    Does 1/n(log(n))^2 converge or diverge

    and therefore it diverges?
  2. G

    Does 1/n(log(n))^2 converge or diverge

    Yes, the integral test, however please tell me how to evaluate this integral? I suspect the result would be some expression that goes to infinity.
  3. G

    Does 1/n(log(n))^2 converge or diverge

    Unfortunately I have never tried the Ei(u) thing. Nor have I heard of integral function. In other words 1/[n(log(n))^2] diverges?
  4. G

    Does 1/n(log(n))^2 converge or diverge

    Most unfortunately both ratio test and limit comparison test give you 1 which is inconclusive.
  5. G

    Does 1/n(log(n))^2 converge or diverge

    No sir, 1/[n(log(n))] diverges, comparison test would not help in this case.
  6. G

    Does 1/n(log(n))^2 converge or diverge

    1. Homework Statement Does 1/[n(log(n))^2] converge or diverge 2. Homework Equations We know that Does 1/[n(log(n))] diverges by integral test 3. The Attempt at a Solution
  7. G

    Why does 1/[nlog(n+1)] diverge

    Yes, however the integral doesn't work in this particular case Note that the question says nlog(n+1), not nlogn
  8. G

    Why does 1/[nlog(n+1)] diverge

    1. Homework Statement Why does the series 1/[nlog(n+1)] diverge 2. Homework Equations We know that 1/[nlog(n)] diverges by the integral test. However the question as written does not lend itself to be any integral precisely. 3. The Attempt at a Solution
  9. G

    Why does 1/[n log(n)]^1.1 converge

    1. Homework Statement Prove that the series: 1/[n log(n)]^1.1 converges 2. Homework Equations 3. The Attempt at a Solution We know that nlogn is equal to d[log(log(n))] and use the integral test to show that it diverges. However, I have no idea how to deal with the 1.1th power.
  10. G

    Sqrt(4n)/sqrt(4n-3)sqrt(4n^2-3n) diverges?

    Yes, comparison test would be great.
  11. G

    Sqrt(4n)/sqrt(4n-3)sqrt(4n^2-3n) diverges?

    1. Homework Statement How to show that sqrt(4n)/sqrt(4n-3)sqrt(4n^2-3n) diverges? 2. Homework Equations 3. The Attempt at a Solution The above expression is asymptotically equivalent to 1/2n which diverges as the harmonic series diverges. However, a rigorous proof is required...
  12. G

    Does limit ln(n)/n^c -> 0 for any c>0?

    Yes, we can use Bolzano Weierstrasse Theorem. Please feel free to proceed. My level is on baby Rudin, the this is the first course in real analysis.
  13. G

    Does limit ln(n)/n^c -> 0 for any c>0?

    Yes, this is for real analysis class
  14. G

    Does limit ln(n)/n^c -> 0 for any c>0?

    1. Homework Statement Does limit ln(n)/n^c -> 0 for any c>0? 2. Homework Equations 3. The Attempt at a Solution I wonder if there is an 1.Epsilon Delta Proof 2.Proof using BigO SmallO notation. Thanks
  15. G

    Does n^2/(n^3+n^2) diverge?

    Is this one more difficult? How do we use the comparison test please to show the following? sqrt[(n^8-10n^3+6)]/{sqrt[(n^7+100n^4+1)]*sqrt[n^3-500n^2+1]}
  16. G

    Does n^2/(n^3+n^2) diverge?

    Please check my answer: for the comparison test, claim that there exists N such that for all n>=N, (n^4-10n^3+6)/(n^5+100n^4+999) >(n^4-10n^3+6)/(2n^5) Proof,need the following n^5+100n^4+999<2n^5 n+100+999/n^4 <2n 100+999/n^4 <n Therefore N=101?
  17. G

    Ln(n)<n^c for all c>0?

    For the comparison test, we need to show that there exists N such that for all n>N ln(n)<Mn^c for some constant M
  18. G

    Does n^2/(n^3+n^2) diverge?

    Sorry I changed my question to (n^4-10n^3+6)/(n^5+100n^4) There is no easy quintic formula so I made up this example to deter any easy way of explicity finding the N
  19. G

    Does n^2/(n^3+n^2) diverge?

    Thanks for the reply. Here is a harder question: (n^4-10n^3)/(n^5+100n^4) It is not obvious that we can explicitly find an N such that for all n>N the above expression is larger than 1/n My point is that is there any rigorous way to show that if lim an= lim bn then series an diverges if and...
  20. G

    Does n^2/(n^3+n^2) diverge?

    1. Homework Statement Does the series n^2/(n^3+n^2) diverge? 2. Homework Equations We know that 1/n diverges 3. The Attempt at a Solution lim n^2/(n^3+n^2) =lim 1/n Therefore intuitively it should diverge like 1/n However, I am not very good at the Big O Small O...
  21. G

    Ln(n)<n^c for all c>0?

    1. Homework Statement How to rigorously (real analysis) prove that for all real c>0 Exists N such that for all n>N ln(n)<n^c 2. Homework Equations 3. The Attempt at a Solution The fact can be shown using graphical calculator
  22. G

    Prove ln(x) < sqrt(x) for all x>0

    Hi, I wonder how to prove that ln(x) < sqrt(x) for all x>0? Please enlighten me on two possible way to prove this . Proof1. Using calculus and derivatives Proof2. Since I'm taking real analysis, I wonder if it is possible to use taylor series to show this in an elegant way.
  23. G

    How to prove ln(x) < sqrt(x) for all x>0

    Except the statement is not true 0.5*1/sqrt(x)-1/x is not always positive for x>0.
  24. G

    How to prove ln(x) < sqrt(x) for all x>0

    Is there a non-graphical way of doing it?
  25. G

    How to prove ln(x) < sqrt(x) for all x>0

    Hi, I know I can use a graphical calculator to easily show that How to prove ln(x) < sqrt(x) for all x>0 But I wonder if there is a rigorous way to demonstrate this.
  26. G

    How to find all complex Z such that Z^5=-32

    t=180degree=-5pi,-3pi,-pi,pi,3pi,5pi,7pi,9pi,11pi? Therefore -32=32*e^(it)=32*[cos(pi)+isin[pi]] Sorry how do I use de Moivre's formula? Never taken complex analysis
  27. G

    How to find all complex Z such that Z^5=-32

    Thank you for your reply. Sorry I do not understand that -32=32*e^(it)? e^it=cost+isint I mean t is a variable that takes on arbitrary values.
  28. G

    How to find all complex Z such that Z^5=-32

    1. Homework Statement How to find all complex number Z such that Z^5=-32 2. Homework Equations Euler equation e^it=cost+isint 3. The Attempt at a Solution I guess a naive way to solve is that since Z^5=(-2)^5 Therefore Z=-2, but this obviously too good to be true. I have no...
  29. G

    Is there a central limit theorem for Median?

    1. Homework Statement Hi, We know the famous central limit theorem for means. I wonder if there is a central limit theorem for Median? If so under what regularity condition, does the median converge to a normal distribution with mean and variance equal to what? 2. Homework Equations...
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