Summation Notation Sec 13 6 Summation Notation o

Summation Notation Sec 13 -6

Summation Notation o Shorthand way of expressing a sum o Uses the Greek letter sigma: ∑ n is called the upper limit of the summation k is called the index of summation ak is the formula used to generate each term of the sum

Summation Notation o Any letter can be used to index a summation n

Summation Notation o Ex: Evaluate the following sum: o Sol:

Summation Notation o Ex: Evaluate the following sum: o Sol:

Summation Notation o Properties (i) (ii) Note: Not true

Summation Notation o Properties (cont) (iii) (iv) for

If the index values are not given, it is understood that the index values could be any values. How do we state a formula to find the mean of a data set, when we don’t know how many data values there?

Example in statistics: o

Standard deviation

SUMMATION NOTATION This number tells us when to stop (the last integer to sub in). This is the formula to sub into This sign means to sum up each of the terms in the sequence This number tells us what integer to start subbing in to create the terms in a sequence Often we want to sum the terms in a sequence so summation notation is a short-hand way express this.

If the top number is an n, write out the sequence summing the terms with a … to the nth term: start by subbing in 0 for the k in the formula

Finally, let’s see if we can go backwards. Given the sum of the terms of the sequence, can we write it using summation notation? Does 2 k - 1 generate these terms subbing in 1 then 2 etc. ? this appears to be the formula with a 12 subbed in

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