Re: inductive reasoning: seven people shake hands w/ each ot
missalissa said:
Seven people meet and shake hands with one another. Using inductive reasoning, write a formula for the number of handshakes if the number of poeple is n.
So far I have (n-1)[n- ] but I'm not sure if that's right or not.
Any help is appreciated! Thank you
Person 1 shakes the hand of 6 people.
Person 2 shakes the hand of 5 peop;e, already having shaked the hand of person 1.
Person 3 shakes the hand of 4 people, already having shaken the hands of persos 1 and 2.
Carrying this to its logical conclusion, the number of hand shakes is 6 + 5 + 4 + 3 + 2 + 1 = 21.
This is simply the sum of the consecutive numbers from 1 to (n - 1), n being the number of people involved.
The formula for the sum of a set of consecutive numbers starting with one is S = n(n + 1)/2.
Since you want the formula in terms of the number of people involved, we make the following adjustment to the formula.
The numer of handshakes of n people is S = (n - 1)((n - 1 + 1))/2 = (n(n - 1)/2.
In your case of 7 people, S = 7(7 - 1)/2 = 21.