Definition of a Sequence

An infinite sequence is a function whose domain is the set of positive integers.
          a1, a2, a3, …, an

If the domain consists of the first n positive integers only, the sequence is finite.

Problems:

Find the first four terms given by an = (-1)n(3n) .  Subsitute 1,2,3, and 4 in for each n .
       a1 = (-1)1(3*1)
       a2 = (-1)2(3*2)
       a3 = (-1)3(3*3)
       a4 = (-1)4(3*4)
 

Summation Notation :

   n
 å   ai = a1 + a2 + a3 + ... + an
i=1
 

   5
 å   k2 = 12 + 22 + 32 + 42 + 52   =   1 + 4 + 9 + 16 + 25   =   55
k=1
 

Properties of Sums :

        n                  n
1.   å   cai =    c å   ai
     i=1                i=1

        n                       n           n
2.   å   ai + bi   =    å   ai + å bi
     i=1                    i=1         i=1
 
 

Problems

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