with a1 = and x>1.Show that it converges and that its limit is x.
hint:Start by using induction to show that this sequence is non-decreasing and bounded above by x.
with a1 = and x>1.Show that it converges and that its limit is x.
hint:Start by using induction to show that this sequence is non-decreasing and bounded above by x.
Take the hint, that shows the sequence converges. Then the limit satisfies the equation:
so
hence or . But the first of these is imposible, so .