7. Let {an} be a sequence of positive real numbers such that an+1/an <= (n+4)/(2n+1) for all n. Then

 

A. 0

B. 1/2

C. 1

D. 2

E. 4

 

Solution: The answer is A

 

By the ratio test, if

then the series

converges, which implies that

Applying the ratio test, yields:

and hence, the series,

is convergent. Consequently