13. Let {an}, {bn}, and {cn} be sequences of positive numbers such that 13. Let {an}, {bn}, and {cn} be sequences of positive numbers such that
Which of the following must be true?
|
A. |
B. |
C. |
|
D. |
E. |
Solution: The answer is E
The following sequences satisfy the given condition.
A. Not true.
Reason:
B. Not true.
Reason:
C. Not true.
Reason:
D. Not true.
Reason:
E. True. Since bn -> 1 we have bn > 1/2 for all n > some number N. Consequently,for n > N, bn cn > (1/2)cn -> infinity.
