You have arrived at summer camp. your counselor has each camper perform a handshake. you and another person are in the cabon so there is one handshake. another person arrives and another and another until there are 14 people in the cabin. how many handshakes will there be in all

think of the situation as a series.

person 1 has to shake hands with 13 other people.

person 2 has to shake hands with 12 other people - he already shook hands with person 1, so there's no need to repeat that.

person 3 has to shake hands with 11 other people - she already shook hands with persons 1 and 2.

person 4 has to shake hands with 10 other people - and so on and so forth, until person 13 only has to shake hands with person 14.

so the total number of handshakes is the sum 13 + 12 + 11 + 10 + + 3 + 2 + 1.

if you remember your arithmetic series, you may recall the formula sn = n(a1 + an)/2. conceptually, this is fairly easy to remember as being the number of terms times the average of the first and last term. the average of the first and last term here is 14/2 = 7, and the total number of terms is clearly 13. the sum should then be 13*7 = 91 handshakes.

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