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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
◄ Previous
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
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