Find the sum of the geometric sequence. three divided by two, three divided by eight, three divided by thirty two, three divided by one hundred and twenty eight, three divided by five hundred and twelve

At a salon, there are nail technicians and hair stylists. the salon owner wants to expand, but can only afford to add no more than 9 new positions. a typical nail technician can see 10 clients per day. a typical hair stylist can see 15 clients per day. the salon owner hopes to be able to see more than 100 clients per day. the new positions constraint is represented by x + y ≤ 9, where x represents the number of nail technicians and y represents the number of hair stylists. find the inequality representing the clients constraint for this situation.