Induction Problems: Solving (n^2-n)/2 & sqrt(n) < 1/sqrt(1)+...+1/sqrt(n)

[guroten]

Homework Statement

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$$\geq$$ 2

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.

 

[slider142]

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?

 

[guroten]

I figured out the first problem, but I'm still having trouble with the second. Any suggestions?

 

[Dick]

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?