We consider the sequence {un} defined by recursion un+1=nun(un+1) for n≥1.
(a) Determine the terms of the sequence for u1=1.
(b) Show that if a member of the sequence is rational, then all subsequent members are also rational numbers.
(c) Show that for every natural number K there is a u1>1 such that the first K terms of the sequence are natural numbers. rationalnumber theoryalgebraSequencerecurrence relation