

1. 
If 6 + 8 + 10 + ··· + (4 + 2n) = n(n + 5), which statement verifies that S_{n} is valid for n = 1? 


A. 
6 + 8 + 10 + 12 = 4(4 + 5); 36 = 36 


B. 
6 + 8 = 2(2 + 5); 14 = 14 


C. 
6 = 1(1 + 5); 6 = 6 


D. 
6 + 8 + 10 = 3(3 + 5); 24 = 24 


Hint 


2. 
If the k term of S_{k} is 4 + 2k, find the (k + 1) term. 


A. 
8 + 2k 
B. 
6 + 2k 


C. 
2k 
D. 
k + 1 


Hint 


3. 
Which of the following is not true about mathematical induction? 


A. 
Mathematical induction depends on a recursive process. 


B. 
The first possible case is always n = 1. 


C. 
Since S_{n} is valid for n = 1, it is valid for n = 2. Since it is valid for n = 2, it is valid for n = 3, and so on, indefinitely. 


D. 
It can be used to prove . 


Hint 


4. 
Which statement would be most logically proven using mathematical induction. 


A. 
Every polynomial has at least one complex root. 


B. 
for all integers n 


C. 
When two parallel lines are cut by a transversal, opposite interior angles are congruent. 


D. 
The series converges. 


Hint 


5. 
If , which statement verifies that S_{n} is valid for n = k + 1? 


A. 



B. 



C. 



D. 



Hint 

