This question has had me stumped for HOURS,I just can't seem to even come close to the answer

the kth term of a series, Sk= A 1-r^k/1-r, is the sum of the first k terms of the underlying sequence. The difference between the nth terms of two particular series is greater than 14 for some values of n E N. The series with the general term Tn= 100(11/17)^n-1 begins larger than the second series with the general term Tn=50(14/17)^n-1 Find the largest natural number,k, where the difference between the terms of these two series is larger then 14.