pamela leutwyler. summation notation is an efficient way to describe a sum of terms, each having the...

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Page 1: Pamela Leutwyler. Summation notation is an efficient way to describe a SUM of terms, each having the same format. Consider the example: Each term has

Pamela Leutwyler

Page 2: Pamela Leutwyler. Summation notation is an efficient way to describe a SUM of terms, each having the same format. Consider the example: Each term has

Summation notation is an efficient way to describe a SUMof terms, each having the same format. Consider the example:

9

8

8

7

7

6

6

5

5

4

4

3

3

2

2

1

Each term has the form

1kk

Page 3: Pamela Leutwyler. Summation notation is an efficient way to describe a SUM of terms, each having the same format. Consider the example: Each term has

Summation notation is an efficient way to describe a SUMof terms, each having the same format. Consider the example:

9

8

8

7

7

6

6

5

5

4

4

3

3

2

2

1

1kk

Take the sum ofall terms of this form

Page 4: Pamela Leutwyler. Summation notation is an efficient way to describe a SUM of terms, each having the same format. Consider the example: Each term has

Summation notation is an efficient way to describe a SUMof terms, each having the same format. Consider the example:

9

8

8

7

7

6

6

5

5

4

4

3

3

2

2

1

1kk

1k

k starts at 1

Page 5: Pamela Leutwyler. Summation notation is an efficient way to describe a SUM of terms, each having the same format. Consider the example: Each term has

Summation notation is an efficient way to describe a SUMof terms, each having the same format. Consider the example:

9

8

8

7

7

6

6

5

5

4

4

3

3

2

2

1

1kk

8

1k

k ends at 8

Page 6: Pamela Leutwyler. Summation notation is an efficient way to describe a SUM of terms, each having the same format. Consider the example: Each term has

Summation notation is an efficient way to describe a SUMof terms, each having the same format. Consider the example:

9

8

8

7

7

6

6

5

5

4

4

3

3

2

2

1

1kk

8

1k

=

Page 7: Pamela Leutwyler. Summation notation is an efficient way to describe a SUM of terms, each having the same format. Consider the example: Each term has

More examples:

n

kkknn

k

k

k

bababababa

k

k

1332211

9

1

1

5

1

2

)1(987654321

2516941

Page 8: Pamela Leutwyler. Summation notation is an efficient way to describe a SUM of terms, each having the same format. Consider the example: Each term has

More examples:

n

kkknn

k

k

k

bababababa

k

k

1332211

9

1

1

5

1

2

)1(987654321

2516941

Page 9: Pamela Leutwyler. Summation notation is an efficient way to describe a SUM of terms, each having the same format. Consider the example: Each term has

More examples:

n

kkknn

k

k

k

bababababa

k

k

1332211

9

1

1

5

1

2

)1(987654321

2516941

Page 10: Pamela Leutwyler. Summation notation is an efficient way to describe a SUM of terms, each having the same format. Consider the example: Each term has

More examples:

n

kkknn

k

k

k

bababababa

k

k

1332211

9

1

1

5

1

2

)1(987654321

2516941

Page 11: Pamela Leutwyler. Summation notation is an efficient way to describe a SUM of terms, each having the same format. Consider the example: Each term has

More examples:

n

kkknn

k

k

k

bababababa

k

k

1332211

9

1

1

5

1

2

)1(987654321

2516941

Page 12: Pamela Leutwyler. Summation notation is an efficient way to describe a SUM of terms, each having the same format. Consider the example: Each term has

More examples:

n

kkknn

k

k

k

bababababa

k

k

1332211

9

1

1

5

1

2

)1(987654321

2516941