Sigma/Summation Notation

5.2

Consider the following sum:

22222 54321 Each of the terms is

in the form of k2, where k is an integer

from 1 to 5.This can be written in sigma notation

as:

5

1

2

k

k

n

n

ii aaaa

...211

Sigma Notation

i -> the index of summation ai -> the ith term i, n -> lower and upper bounds of

summation

Determine the sum

4

1

2k

k )24()23()22()21(

6543

18

Determine the sum

5

3

3k

k )5(3)4(3)3(3

15129

36

Determine the sum

4

0

)12()1(k

k k

1)4(211)3(211)2(211)1(211)0(21 43210

97531

5

Determine the sum

4

1

)sin(k

k

)4sin()3sin()2sin()1sin(

0000

0

Summation Properties

n

kk

n

kk acca

11

n

kk

n

kk

n

kkk baba

111

n

k

ncc1

Useful Theorems

2

1...321

1

nnnk

n

k

6

121...321

1

22222

nnnnk

n

k

4

1...321

22

1

33333

nnnk

n

k

Determine the sum

12

1

22i

i

6

)1)12(2)(112(122

1300

12

1

22i

i

6

)25)(13(122

Determine the sum

6

1

2 1i

i

66

)13)(7(6

97

6

1

6

1

2 1ii

i

Determine the sum

6

1

22i

i

)6(42

)7(64

6

)13)(7(6

199

6

1

6

1

6

1

2 44iii

ii