Series F(n) is such that i*F(i) = j*F(j) for any pair of positive integers (i, j). If F(1) is a positive integer, which of the following is possible?
I. 2*F(100) = F(99) + F(98)
II. F(1) is the only integer in the series
III. The series does not contain negative numbers
Select the correct option:	A) I only	B) II only	C) IIII only	D) IIIII only	E) I, IIIII
First thing I want to understand is this relation: i*F(i) = j*F(j) for any pair of positive integers. I will take examples to understand it.   When i = 1 and j = 2, F(1) = 2*F(2)   So F(2) = F(1)/2   When i = 1 and j = 3, F(1) = 3*F(3)   So F(3) = F(1)/3   I see it now. The series is: F(1), F(1)/2, F(1)/3, F(1)/4 and so on...   II and III are easily possible. We can see that without any calculations.   II. F(1) is the only integer in the series   If F(1) = 1, then series becomes 1, 1/2, 1/3, 1/4 ... all fractions except F(1)   III. The series does not contain negative numbers   Again, same series as above applies. In fact, since F(1) is a positive integer, this must be true.   I. 2*F(100) = F(99) + F(98)   2*F(1)/100 = F(1)/99 + F(1)/98 (cancel F(1) from both sides)   2/100 = 1/99 + 1/98   Not true hence this is not possible   Answer (IIIII only)
<result>D</result>
Series F(n) is such that i*F(i) = j*F(j) for any pair of positive integers (i, j). If F(1) is a positive integer, which of the following is possible?
I. 2*F(100) = F(99) + F(98)
II. F(1) is the only integer in the series
III. The series does not contain negative numbers