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Induction problems

  1. Feb 7, 2009 #1
    1. The problem statement, all variables and given/known data
    show that for n points in a plane, with no 3 points colinear, the number of line segments joining all pairs of points is (n^2-n)/2


    Problem 2
    Show that sqrt(n) is strictly less than 1/sqrt(1) +1/sqrt(2)+...+1/sqrt(n) for n[tex]\geq[/tex] 2


    3. The attempt at a solution
    For problem 1, I have no idea how to start. For problem 2, I tried manipulating the equation and substituting in the induction assumption, but I couldn't get anywhere with it.
     
  2. jcsd
  3. Feb 7, 2009 #2
    Suppose you already have n points all joined up and you add a point somewhere else not joined to any other point. How many lines do you have to draw to connect this one point to every point in the existing diagram?
     
  4. Feb 8, 2009 #3
    I figured out the first problem, but I'm still having trouble with the second. Any suggestions?
     
  5. Feb 8, 2009 #4

    Dick

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    You haven't shown us what you did, so we don't know what your problem is. What do you need to prove to make the induction work?
     
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