It is one of the two sums that go to infinity. The other two will end in some sort of sum even though r is > 1 in D and < -1 in B. The answer will likely be quite nasty in both of them, still they will end somewhere.
That leaves with A and C.
A: will converge somewhere - 1 <r <1 converges when that condition about r is true and you can get a sum.
C the one that does not converge anywhere. 4/3 raised to a large power gives a very large number which never gets smaller and the sum is indefinite getting larger and larger as i increases. C is your answer.
The length of the rope for this case is given by the length of the circumference. We have then: C = 2 * pi * R Where, R: Earth radio. We have then: C = 2 * pi * (6371) C = 12742 * pi Answer: the length of this rope is: C = 12742 * pi
