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.

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i2

i=1

6

∑i is called the index of the summation1 is the lower limit of the summation6 is the upper limit of the summation

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∑is the sigma symbol and means add it up

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i2

i=1

6

∑ = 12+22+ 32+ 42+52+62

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=1+4+9+16+25+ 36

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=91The upper and lower limits can be any positive integer or zero.The index can be any variable

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(2k +1)k=3

5

∑€

= 23 +1( ) + 24 +1( ) + 2

5 +1( )

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= 8+1( ) + 16+1( ) + 32+1( )

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= 9 +17 + 33

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= 59

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(2i + j)j=1

4

∑

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= 2i+1( ) + 2i+2( ) + 2i+ 3( ) + 2i+ 4( )

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=8i + 10

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5i=3

11

∑

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=5+5+5+5+5+5+5+5+5

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=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:

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a1 =1, a2 =1 and an = an−1 +an−2 for n ≥ 3

Fibonacci!

Using

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an =, notation, write a definition for the sequences below.

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a) 3, 6, 9, 12, . . .

b)2

5,

3

25,

4

125,5

625. . .

c) 8, 8, 8, 8, . . .

CAN #6 Sequences/Sums on the CalculatorPractice #3: p. 934 18-42 evens, 43-51 odds, 61-65 odds, 73