IB MATEMATICS Topic : Sequences and Series – The Summation Notation

Sequences and Series – The Summation Notation

The symbolmeans add. It is usually used to add a sequence of numbers, called a series – the summation of a series of numbers is called a series.

The summation is usually defined in terms of some variable(the letteris arbitrary. It may be any letter, still denoting integer values). The variable may take any value between certain limits, indicated above and below the summation symbol.

Consider the sequencefor which the rule is

The notationmeans add up up the numbersfor all the integer values of betweenand

The notation is not unique.



all mean the same thing, and this list of examples is not exhaustive.
All the example above are of the same arithmetic sequenceThese terms are generated by the rulewhich defines the sequence and appears the summations above.
We may also define a summation in terms of recurrence relation, which uses a rule to obtain the next term from the present term – for example,To obtain the next term, add 3 to the present term.
The above example is of an arithmetic sequence. In fact a wide range of series may be so treated. Any series defined by a recurrence relation and geometric series too, which obtains that next term by multiplying the present term by a constant factor. If

then
may be found by evaluating each term and adding.
and
Adding these gives