Lesson 3 Sums of Series Notes.ppt gcse tutorial

Slide for series tutorial for up to gcse category

1. Arithmetic and Geometric
Series and Sigma Notation
Advanced Math Topics
Mrs. Mongold

2. What is a series?
When the terms of a sequence are added,
the indicated sum of the terms is called a
series.
Example
Sequence 1, 2, 3, 4, 5, 6
Series 1+2+3+4+5+6

3. Types of Series
Finite Series
Has a last term…. Ends in a number
Infinite Series
Doesn’t have a last term…. Ends in …
Arithmetic Series
When the terms form an arithmetic sequence

4. General Equation for the Sum of a finite
arithmetic series2
)(
1 naan
S


Number
Of terms
In series
Value of
First
term
Value of
Last
term

5. Let’s practice…
1, 2, 3, 4, 5, 6
n = 6
a
1=1
a
n=6

6. Find the sum of 7+12+17+22+…+52
1. Identify type of sequence
2. Write the explicit formula
3. Find the number of terms in the sequence
4. Plug in the values and solve the formula

7. Find the sum of 2+4+8+…+128
1. Identify the type of sequence
2. Write the explicit formula
3. Find the number of terms in the sequence
4. Plug in the values and solve the formula

8. Sigma Notation
Compact form for series
Uses the summation symbol Σ
Greek letter sigma

9. Sigma Notation 
Explicit formula for
the related sequence
Number of terms in series
First value of n

10. For our sequence 1, 2, 3, 4, 5, 6
6
n=1
n

11. Let’s Practice
Go back to example 1
and write it sigma
notation
7+12+17+22+…+52
Need number of
terms
Value of first term
Value of n

12. Evaluate
8
n=1
5-2n

13. Evaluate
7
n=2
|4 –n|

14. Write the series in sigma notation
7+10+13+16+…+64
First identify type of series and any important
values (d or r) then find the explicit formula and
the number of terms.

15. Day 2 Notes Starts Here

16. Geometric Series
When the terms of a series form a
geometric sequence
Remember geometric sequences have a
pattern of multiplying each term by the same
number to get the next term in the sequence

17. Example of Geometric Series
NCAA tournament…
64 teams to start
Sequence looks like this
32, 16, 8, 4, 2, 1
Series looks like this
32+16+8+4+2+1

18. Short cut way to find Sum for
Geometric Sequencer
raa
S
n



1
1

19. Example
Going back seven generations, how many biological ancestors do you
have? Count your parents as the first generation, your four grandparents as
the second and so on.

20. Sigma Notation
Works the same way as an arithmetic series
but will be in the explicit form for geometric
series which is1
1


n
nraa

21. Example
(-1) + 3 + (-9) + 27 + (-81) + 243 + (-729) + 2187

22. Example
2 + 4 + 8 + 16 + 32 + 64 + 128

23. Example
8 + 4 + 2 + 1 + ½ + ¼