1. Summation Notation
Sec 13-6

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

3. Summation Notation
Any letter can be used to index a summation

4. Summation Notation
Ex: Evaluate the following sum:
Sol:

5. Summation Notation
Ex: Evaluate the following sum:
Sol:

6. Summation Notation
Properties
(i)
(ii)
Note: Not true

7. Summation Notation
Properties (cont)
(iii) for
(iv)

8. 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?

9. Example in statistics:
To find the mean of any data set: 𝑚𝑒𝑎𝑛= 𝑠𝑢𝑚 𝑜𝑓 𝑎𝑙𝑙 𝑑𝑎𝑡𝑎 𝑣𝑎𝑙𝑢𝑒𝑠 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑡𝑎 𝑣𝑎𝑙𝑢𝑒𝑠 Symbolically: 𝑚𝑒𝑎𝑛= 𝑥 𝑛

10. Standard deviation

11. 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.

12. 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

13. Finally, let’s see if we can go backwards
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 2k - 1 generate these terms subbing in 1 then 2 etc.?
this appears to be the formula with a 12 subbed in

14. On your calculator:
click here for instructions on your calculator