The given data contains points which are 1/5, 1/25, 1/125, and 1/625. From these we are able to conclude that the given is a geometric sequence with r equal to 1/5 and the first term is equal to 1/5. The sum of these term can be computed as,
S = a1/(1 - r)
Solving,
S = ((1/5)/(1 - 1/5) = 1/4
Thus, the sequence is convergent because the sum is a finite number.