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Series

A series is the indicated sum of the terms of a sequence.

Example 1:

Finite sequence            : 3,7,11,15,19

Related finite series      : 3+7+11+15+19

Infinite sequence          : 1 2 , 1 4 , 1 8 , 1 16 ,

Related infinite series   : 1 2 + 1 4 + 1 8 + 1 16 +

A series can be written in an abbreviated form by using the Greek letter (sigma), called the summation sign.  For instance, to abbreviate the writing of the series 2+4+6+8++50 first notice that the general term of the series is 2n .  The series begins with the term for n=1 and ends with the term for n=25 .  Using sigma notation, you can write this series as n=1 25 2n , which is read “the sum of 2n for values of n from 1 to 25 .”

n=1 25 2n =21+22+23+24++225 =2+4+6+8++50

There are formulas to help you quickly find the value of finite arithmetic series, finite geometric series, and certain kinds of infinite geometric series.

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