Recent content by dianetics

  1. D

    If a sequence converges to L, so the the sequence of averages

    I'm not following. Why do we only care about the terms of xn for sufficiently large n? yn is dependent on all x1...xn-1 as well. Edit: I have this so far: the convergence of x_n means that: | (x_n + x_n+1 + ... + xm) / (m - n + 1) - L | < e Now I'm trying to incorporate ym somehow into this...
  2. D

    If a sequence converges to L, so the the sequence of averages

    How does this imply the convergence of y_n?
  3. D

    If a sequence converges to L, so the the sequence of averages

    No, lol...
  4. D

    If a sequence converges to L, so the the sequence of averages

    Homework Statement ( xn ) is given. ym = ( x1 + . . . + xm ) / m show that if xn converges to M, then ym converges to M Homework Equations Definition of convergence for sequences The Attempt at a Solution I've tried a whole page full of algebraic manipulation. I found a recursive...