
Math Induction HW
hey all,
I'm on my last problem and I'm stuck. I think it is just too late, but i desperately want to finish this today. Anyhow here is what it reads:
In any group of k people, k>=1, each person is to shake hands with every other person. Find a formula for the number of handshakes, and prove the formula using induction.
Once i get the formula the proof is cake, but the formula is driving me crazy, and it is probably very simple.
so here is what I have
Code:
1 person = 0 shakes
2 people = 1 shake
3 people = 3 shakes
P(4) = 6
P(5) = 10
P(6) = 15
...and so on
can anyone put me on the right track?
thanks,
axon

I finally found the formula so please disregard this post!
for all interested here it is: k( k 1 ) / 2 for k >=1
so simple!!!:o :o and it took an hour of my life

Damn i was alogn those lines workign on it, ah well shoulda given me another 5 minutes

thanks anyways: if you want I have one for extra credit, here goes:
A simple closed polygon consists of n points in the plane joined in pairs by n line segments: each point is the endpoint of exactly two line segments. Use the first and second principal of induction to prove that the sum of the interior angles of an nsided closed polygon is ( n  2 ) 180degrees for all n >= 3.
I'll work on this one now, until I'm too sleepy to do anymore.

well, this one was fairly simple...the proof below is using the second principal of induction:
Code:
when k = 3, we have a triangle. Sum of all angles = 180° so
for each n > 3, if P(k) is true for all k with 3 <= k < n, then P(n) is true.
180°(k2) + 180°[(nk+2)2] = 180°(k2) +180°(nk)
= 180°[(k2) + (nk)]
= 180°(n2) => DONE
basically you can divide each ksided polygan with k3 lines to form
triangles. Multiply the number of triangles by 180°....simple