Show that the sequence (xn) defined by x1=1andxn+1=1xn+3(n=1,2,…) converges and determine its limit ?
I try to show (xn) is a Cauchy sequence or (xn) is decreasing (or increasing) and bounded sequence but I fail every step of all.
Answer
Hint: For x,y≥0 we have |1x+3−1y+3|=|y−x(x+3)(y+3)|≤19|x−y|.
No comments:
Post a Comment