A tank contains 1000 litres of pure water. Brine with 0.05 kilograms of salt per litre of water enters the tank at a rate of 5 litres per minute. Brine that contains 0.04kg of salt per litre of water enters the tank at a rate of 10 litres per minute. The solution is kept thoroughly mixed and drains from the tank at a rate of 15 litres per minute. How much salt is present a) after t minutes? b) after one hour? Consider the sequence {a} given by 4n-1 an with n = 1,2,3,... 4n a) Is the sequence {a} monotone? Justify your answer. b) Show that the sequence {a} converges. Find the limit of the sequence an = (2n+3)(n-1) n(n+1) By using the comparison test, decide if the following series converges: n=1 an = n=1 If it does converge, find its limit. (n+4)(n-1) n(n + 1)