Sigma/Summation Notation 5.2

Sigma/Summation Notation 5.2

Consider the following sum: 2 2 2 2 1 2 3 4 5 This can be written in sigma notation as: 5 2 k k 1 2 Each of the terms is in the form of k2, where k is an integer from 1 to 5.

Sigma Notation n a i a1 a2 . an i 1 i is the index of summation ai is the ith term i and n are the lower and upper bounds of summation

Determine the sum 4 k 2 (1 2) (2 2) (3 2) (4 2) k 1 3 4 5 6 18

Determine the sum 4 k 2 (1 2) (2 2) (3 2) (4 2) k 1 3 4 5 6 18

Determine the sum 4 k 2 (1 2) (2 2) (3 2) (4 2) k 1 3 4 5 6 18

Determine the sum 5 3k 3(3) 3(4) 3(5) k 3 9 12 15 36

Determine the sum 5 3k 3(3) 3(4) 3(5) k 3 9 12 15 36

Determine the sum 5 3k 3(3) 3(4) 3(5) k 3 9 12 15 36

Determine the sum 4 k ( 1 ) (2k 1) k 0 0 1 2 3 4 1 2(0) 1 1 2(1) 1 1 2(2) 1 1 2(3) 1 1 2(4) 1 1 3 5 7 9 5

Determine the sum 4 k ( 1 ) (2k 1) k 0 0 1 2 3 4 1 2(0) 1 1 2(1) 1 1 2(2) 1 1 2(3) 1 1 2(4) 1 1 3 5 7 9 5

Determine the sum 4 k ( 1 ) (2k 1) k 0 0 1 2 3 4 1 2(0) 1 1 2(1) 1 1 2(2) 1 1 2(3) 1 1 2(4) 1 1 3 5 7 9 5

Determine the sum 4 k ( 1 ) (2k 1) k 0 0 1 2 3 4 1 2(0) 1 1 2(1) 1 1 2(2) 1 1 2(3) 1 1 2(4) 1 1 3 5 7 9 5

Determine the sum 4 sin( k ) k 1 sin(1 ) sin( 2 ) sin(3 ) sin( 4 ) 0 0 0 0 0

Determine the sum 4 sin( k ) k 1 sin(1 ) sin( 2 ) sin(3 ) sin( 4 ) 0 0 0 0 0

Determine the sum 4 sin( k ) k 1 sin(1 ) sin( 2 ) sin(3 ) sin( 4 ) 0 0 0 0 0

Determine the sum 4 sin( k ) k 1 sin(1 ) sin( 2 ) sin(3 ) sin( 4 ) 0 0 0 0 0

Summation Properties n ca k 1 n k c ak k 1 n a k 1 n n k bk ak bk c nc k 1 n k 1 k 1

Useful Theorems n n 1 k 1 2 3 . n 2 k 1 n n n 1 2n 1 k 1 2 3 . n 6 k 1 n 2 2 2 2 2 2 n n 1 k 1 2 3 . n 4 k 1 n 3 3 3 3 3 2

Determine the sum 12 2 2 i i 1 12 2 i 2 i 1 12(12 1)(2(12) 1) 2 6 12(13)(25) 2 6 1300

Determine the sum 12 2 2 i i 1 12 2 i 2 i 1 12(12 1)(2(12) 1) 2 6 12(13)(25) 2 6 1300

Determine the sum 12 2 2 i i 1 12 2 i 2 i 1 12(12 1)(2(12) 1) 2 6 12(13)(25) 2 6 1300

Determine the sum 12 2 2 i i 1 12 2 i 2 i 1 12(12 1)(2(12) 1) 2 6 12(13)(25) 2 6 1300

Determine the sum 12 2 2 i i 1 12 2 i 2 i 1 12(12 1)(2(12) 1) 2 6 12(13)(25) 2 6 1300

Determine the sum 6 i i 1 2 1 6 6 i 1 i 1 i 2 1 6(7)(13) 6 6 97

Determine the sum 6 i i 1 2 1 6 6 i 1 i 1 i 2 1 6(7)(13) 6 6 97

Determine the sum 6 i i 1 2 1 6 6 i 1 i 1 i 2 1 6(7)(13) 6 6 97

Determine the sum 6 i i 1 2 1 6 6 i 1 i 1 i 2 1 6(7)(13) 6 6 97

Determine the sum 6 i 2 i 1 2 6 6 6 i 1 i 1 i 1 i 2 4 i 4 6(7)(13) 6(7) 4 4(6) 6 2 199

Determine the sum 6 i 2 i 1 2 6 6 6 i 1 i 1 i 1 i 2 4 i 4 6(7)(13) 6(7) 4 4(6) 6 2 199

Determine the sum 6 i 2 i 1 2 6 6 6 i 1 i 1 i 1 i 2 4 i 4 6(7)(13) 6(7) 4 4(6) 6 2 199

Determine the sum 6 i 2 i 1 2 6 6 6 i 1 i 1 i 1 i 2 4 i 4 6(7)(13) 6(7) 4 4(6) 6 2 199

Homework Online book lesson 4.2 Section Exercises 1-20