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