ABSTRACT
Frequently we may be interested in finding the sum of several observations» For example, in a class of 50 students, we may wish to determine the average student age. To do this we would record the age of each student, sum the ages and divide by 50. How can we express this series of operations in a general and compact way? Let xx be the age of the first student on the class roster, x2 the age of the second, and so on with Xgo representing the age of the fiftieth student. The sum then is
x 1 + x2 + • • • + Xgo ,
where • • • indicates "and so on ." Using the Greek letter ZJ (sigma) as a symbol for summation, we can obtain an even more compact representation:
This expression is read "sum of x sub i where i goes from 1 to 50." The letter i under the summation sign 2 is called the index of summation» It takes on all integral values from its lower limit written below the sigma to its upper limit written above the sigma. Any letter may be used for the index, e .g . , i, j, k or i .
