Recent content by jeff1evesque

  1. J

    Java Javascript/JQuery Nav Button Highlighting

    Yeah I used CSS to get the buttons to highlight and stuff. But as the button background changes color upon the mouse being over it, the text doesn't change- even though I specified it to change to white (in the CSS: navbar.css): div.nav a:hover { color:white; background:#404040; }So, I am not...
  2. J

    Java Javascript/JQuery Nav Button Highlighting

    I am writing a small personal webpage (http://pubpages.unh.edu/~jmm42/JML/levesque.html# ), and am trying to write code so that when the cursor is over my navigation buttons, the buttons highlight to a gray color #404040: and the text color becomes white. I am trying to write this code in...
  3. J

    Prove: x_m Is Not Bounded Above, x_m Does Not Converge

    Homework Statement Let x_m = 1 + \frac{1}{2} + \frac{1}{3} + ... \frac{1}{m}, m \in N. Prove x_m is not bounded above and therefore x_m does not converge.Homework Equations We know from our class an important theorem stating that: If sequence converges then the sequence is bounded. Thus we...
  4. J

    Inequality Proof Homework: Proving 2^k+1 $\geq$ 1/2

    never minnd, I actually did this in a different problem- thanks everyone
  5. J

    Inequality Proof Homework: Proving 2^k+1 $\geq$ 1/2

    2^k terms.
  6. J

    Inequality Proof Homework: Proving 2^k+1 $\geq$ 1/2

    There are 2^{k+1} terms
  7. J

    Inequality Proof Homework: Proving 2^k+1 $\geq$ 1/2

    Yes I agree, but that isn't helping me at all- I just don't know how to formulate a proof for this.
  8. J

    Inequality Proof Homework: Proving 2^k+1 $\geq$ 1/2

    I still don't see it, i wish it were clear to me. Thanks though, Jeffrey Levesque
  9. J

    Inequality Proof Homework: Proving 2^k+1 $\geq$ 1/2

    Homework Statement \frac{1}{2^{k}+1} + \frac{1}{2^{k} +2} + ... + \frac{1}{2^k + 2^k} \geq \frac{1}{2} 2. The attempt at a solution Not too sure, I am working on a larger proof (not too much difficult) and the above is my attempt to prove the induction step k+1 (since \frac{1}{2^k + 2^k} =...
  10. J

    Undergrad Proving the Convergence of (2n^2+n)/(n^2) to 2

    Yeah that's it. Except i was just given sequence (2n^2+n)/(n^2) --> 2. And in my idea stage, I have the sequence equal to 1/(2^n - n) < 1/n.. and this is only true if n > 2.
  11. J

    Undergrad Proving the Convergence of (2n^2+n)/(n^2) to 2

    I need to show 2^n - n > n But I need to start the proof with the assumption that n > 2.
  12. J

    Undergrad Proving the Convergence of (2n^2+n)/(n^2) to 2

    Exactly what i was thinking, but i need it in a different form to fit my proof. Proof: Let e > 0 be given. Let N = max{2, 1/n} Note that, |1/(2^n - n) - 0| = |1/(2^n - n)| (trying to show later in the proof this is less than 1/n) Assume n > N then n > 2 (Goal: show that 1/(2^n - n) <...
  13. J

    Undergrad Proving the Convergence of (2n^2+n)/(n^2) to 2

    I am trying to prove a larger problem, that the sequence (2n^2+n)/(n^2) --> 2 however, i need something small to prove it which is proving the fact that given n > 2, 2^n - n > n THanks, JL
  14. J

    Proving Continuous Functions Cannot Be Two-to-One

    Homework Statement Suppose f: [0,1] \rightarrow R is two-to-one. That is, for each y \in R, f^{-1}({y}) is empty or contains exactly two points. Prove that no such function can be continuous. Homework Equations Definition of a continuous function: Suppose E \subset R and f: E...
  15. J

    Continuity and liimit of functions

    Can someone provide some insight for me as to what the following means: And how I could use this fact to construct my justification for whether f is necessarily continuous?