I would appreciate having a solution written with nice handwriting and detail explanations

(6) Recall that a real number is called a Liouville number if and only if for every n > 1 there exists P,q Z,q > 2, such that O 0 be given. Explain why we can find a positive integer n > 1 such that E qn_l 2, such 1 1 3 3 that 0