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From above I will need work for one question from the partial fraction section in the next 8 hours for an attendance discussion post. I will also need work for one problem from the sequence work section. I will also need fork for question 5 of the qu iz. The rest I only need answers. For the the first attachment you can choose one of the problems to do. I will also need work for these two questions.

9.

Verify the following identity:

10. Find all missing measures

m/C=31°, b = 32 yd, c = 27 yd

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10

1

1+ sin x

1

1-sin x

2 sec² x

7

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In Exercises 13-20, use mathematical induction to prove that the state-

ment holds for all positive integers.

13. 1 + 5 +9+ + (4n

14. 1 + 2 +2²+…+ 2²-1

1

15.

1

+

1.2 2.3

1

+

1.3 3.5

16.

+

+

17. 1+ 2+ 3+

1

3.4

18. 1²+ 2² + 3² +

19. 1³ + 2³ +3³ +

20. 1ª + 24 + 34 +

+

72. 1+3+ 6 + … +

(2n 1)(2n + 1)

3) = n(2n − 1)

= 2″ 1

1

n(n + 1)

+ n =

+

=

76. 1 +5 + 9 + … + (4n

+ n²

+ n²

1

2″

n(n + 1)

2

–

2

+ n²

n(n + 1) (2n + 1) (3n² + 3n − 1)

30

In Exercises 71-76, use mathematical induction to prove the statement.

1

1

71. 1+ =+=+…+

2 4

–

=

1

2″

=

=

n(n+1)

2

n(n + 1) (2n + 1)

6

n² (n + 1)²

4

73. (n + 1)² + n is odd.

74. n³ + 2n is divisible by 3.

3

75. 3+ 6 +9+ + 3n = n(n + 1)

n

n+ 1

n

2n + 1

3) = n(2n 1)

n(n + 1)(n + 2)

6