Transcript Factorial and Summation Notation

Factorial Notation
For any positive integer n, n! means:
n (n – 1) (n – 2) .
.
.
(3) (2) (1)
0! will be defined as equal to one.
Examples:
4! = 4•3 •2 •1 = 24
The factorial symbol only affects the number it follows
unless grouping symbols are used.
3 •5! = 3 •5 •4 •3 •2 •1 = 360
( 3 •5 )! = 15! = big number
Summation Notation is used to represent a sum.
1, 4, 9, 16, . . .
Add the first six terms of the above sequence.
1 + 4 + 9 + 16 + 25 + 36 = 91
Summation Notation can be used to represent this
sum.
6
i
2
i1
i is called the index of the summation
1 is the lower limit of the summation
6 is the upper limit of the summation
 is the sigma symbol and means add it up
6
i
2
 12 2 2  32  4 2  5 2  6 2
 14 916 25  36
 91
The upper and lower limits can be any positive integer or

zero.

The index can
 be any variable
i1
5
 (2
k 3
k
 1)


 2 3 1  2 4 1  25 1
 8 1  161  321
 9 17  33
 59
4
 (2i  j)  2i 1  2i  2  2i  3  2i  4
j1
 8i  10


11
5


i3

 555555555
 45
 The number of terms in a summation is:
 upper limit – lower limit + 1
Practice #2: p. 934-935 19-41 odds
Find the first 6 terms of the sequence defined as:
a1 1, a2 1 and an  an1  an2

Fibonacci!
for n  3
Using an , notation, write a definition for the sequences below.
a) 3, 6, 9, 12, . . .

2
b) ,
5
3
4
5
,
,
. . .
25 125 625
c) 8, 8, 8, 8, . . .
CAN #6 Sequences/Sums on the Calculator

Practice #3: p. 934 18-42 evens, 43-51 odds,
61-65 odds, 73