SOLUTION: 7 people meet and shake hands with one another, how many handshakes occurred? using inductive reasoning, wrte a formula for the number of handshakes if the number of people is n

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Question 485051: 7 people meet and shake hands with one another, how many handshakes occurred?
using inductive reasoning, wrte a formula for the number of handshakes if the number of people is n.
the Fibonacci sequence consists of the pattern 1,1,2,3,5,8,13,...., what is the ninth term in the pattern?
look at the successive ratios of ne term to the next, make a conjecture?
list the first eight terms of the sequence formed by finding the differences of sucessive terms in the fibonacci sequence?
Answer by solver91311(24713) (Show Source):
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The first of the 7 people will shake hands with 6 others. Only 6 because no person is going to shake hands with themselves. The second person also shakes hands with 6 people, but you have already counted one of those handshakes, namely the one with the first person. Therefore, the second person shakes hands with only 5 NEW people. Then the third person adds 4 new handshakes, etc., down to the 2nd to the last person who adds 1 new handshake. The last person has no one new, so all of the last person's handshakes are already counted. In summary:

If you have people, then follow the same pattern:

Or put more succinctly using sigma notation:

John

My calculator said it, I believe it, that settles it