Sequences Series Part2

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Contents 1 Summation Notation 1.1 Examples 1.2 Examples 2 Writing Series using 3 Exercise 2

Summation Notation

• is read as
  • sum
  • sum of
  • sum of from
  • sum of from to (note that is not written at the top part as it it unnecessary)

Now let's see how to write out the sum

• 
  • We can see from the above, that this means
    • the sum of all the 's, from
    • , meaning from
    • to , meaning to
  • In others words, sum from to
  • 

Notes

• have the same meaning, but is usually only used in AP & GP
• In sequences, we used to represent the general term, that is, any term in the sequence.
• In series, however, is reserved for the last term only. Thus, for the general term, we need to use another alphabet, thus we use
• General term represented by
  • 

Examples

• 
  • 

• 
  • You can see that this notation is more flexible than in that it allows to start from any integer and not just from

• 
  • 

• 
  • 

Furthermore, this notation allows us to write exactly what is right at the notation (compared to where have to be written seperately

Examples

• 
  • Note that goes into , starting from to

• 
  • 

• 
  • It's best NOT to write but instead count it directly, but carefully.

• 

Writing Series using

To be able to write a series using the notation , we must

• determine Note that we usually choose an so that it the series starts with
• determine

Exercise 2

1) Write out the following sums

• a)

• b)

• c)

• d)

• e)

2) Express the following using notation

• a)
  • 

• b)
  • 

• c)
  • 

• d)
  • 

• e)
  • 

• f)
  • 

• g)
  • 

• h)
  • 

• i)
  • 

• j)
  •