Recent content by jbear12

  1. J

    Calculating the Limit of n!^(1/n) and (1/n)(n!)^(1/n)

    anyone?
  2. J

    Calculating the Limit of n!^(1/n) and (1/n)(n!)^(1/n)

    it works now :D
  3. J

    Calculating the Limit of n!^(1/n) and (1/n)(n!)^(1/n)

    I mean the hint theorem
  4. J

    Calculating the Limit of n!^(1/n) and (1/n)(n!)^(1/n)

    Hi Senjai Can you tell me what's wrong with my code? I spent half an hour editing this and it only displays the first part...I have a midterm tomorrow :(
  5. J

    Calculating the Limit of n!^(1/n) and (1/n)(n!)^(1/n)

    Anyone?
  6. J

    Calculating the Limit of n!^(1/n) and (1/n)(n!)^(1/n)

    The problem is to caculate the limit for: lim n!^{\frac{1}{n}} and lim {\frac{1}{n}} (n!)^{\frac{1}{n}} Hints to this problem are the theorem: lim inf |\frac{Sn+1}{Sn}| \leq lim inf |Sn|^{\frac{1}{n}} \leq lim sup |Sn|^{\frac{1}{n}} \leq lim sup |{\frac{Sn+1}{Sn}}| and lim...
  7. J

    Proving Binomial Coefficients for Even n | Combinatorial Argument

    Thanks HallsofIvy. But I don't get it how you get from C(n, 2k)= C(n-1,2k)-C(n-1, 2k-1) to C(n, i)= C(n-1, i)+ C(n-1, i). Taking i=2k, why is C(n-1,i-1) equal to -C(n-1,i). Also, why is \sum_{i= 0}^n C(n-1, i)= 2* \sum_{i= 0}^{n/2} C(n-1, i)
  8. J

    Proving Binomial Coefficients for Even n | Combinatorial Argument

    Suppose n is even, prove: \sumk=0->n/2, C(n,2k)=2^(n-1)=\sumk=1->n/2, C(n,2k-1) Give a combinatorial argument to prove that: (I've figured out this one...) \sumk=1->n, C(n,k)^2=C(2n,n) For the first problem, I tried to break C(n, 2k) into C(n+1,2k)-C(n, 2k-1), but they didnt seem to work very...
  9. J

    Proving Inner Product Space: x not in W, y in W(perp)

    Umm..I don't really get it. Can you explain more specifically? Thank you.
  10. J

    Proving Inner Product Space: x not in W, y in W(perp)

    Let V be an inner product space, and let W be a finite-dimensional subspace of V. If x\notin W, prove that there exists y\in V such that y \in W(perp), but <x,y>\neq 0. I don't have a clue... Thanks
  11. J

    Gram-schmidts orthonormalization

    I get it. Thank you very much, lanedance. :)
  12. J

    Gram-schmidts orthonormalization

    Thank you lanedance. I realized it after some searching on the internet. :) I have another dumb question...:P What's the length of (1-5i/2, 7-i/2,4i)? Is it the square root of (1-5i/2)squared+(7-i/2)squared+(4i)squared, where i2=-1?
  13. J

    Gram-schmidts orthonormalization

    Apply Gram-Schmidts process to the sebust S of the inner product space V to obtain an orthogonal basis for span(S). Then normalize the vectors in this basis to obtain an orthognormal basis for span(S) V=span(S) where S={(1,i,0), (1-i,2,4i)} and x=(3+i,4i,-4). Isn't the length of (1,i,0)...