Final answer:
An example of a sequence of irrational numbers converging to a rational number is provided, as well as an example of a sequence of rational numbers converging to an irrational number.
Step-by-step explanation:
(a) Here's an example of a sequence (xn) of irrational numbers that converge to a rational number: Let's consider the sequence (sqrt(2), sqrt(2)/2, sqrt(2)/4, sqrt(2)/8, ...). Each term in this sequence is irrational, but as we keep dividing by 2, the terms get closer and closer to 0, which is a rational number.
(b) As for a sequence (rn) of rational numbers that converge to an irrational number, consider the sequence (1, 1.4, 1.41, 1.414, ...). In this sequence, each term is rational, but as we keep adding more decimal places to the square root of 2, the terms get closer and closer to the irrational number sqrt(2).