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 i1 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 i1 1 4 916 25 36 91 The upper and lower limits can be any positive integer or zero. The index can be any variable 5 (2 k 3 k 1) 2 3 1 2 4 1 2 5 1 8 1 16 1 32 1 9 17 33 59 4 (2i j) 2i 1 2i 2 2i 3 2i 4 j1 8i 10 11 5 i3 555555555 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 an1 an2 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