Convergence 1(40points ！！！)

a) Given that (∞Σn=1)an converges and an≧0 for any n belongs to Natural numbers.
i) Prove that there exists N(which is belongs to Natural numbers) such that for any n (Natural numbers) if n >N then 0≦an^2≦an. 20 points
ii) Prove that (∞Σn=1)an^2 converges.

part b 可到以下網址找到：
http://hk.knowledge.yahoo.com/question/?qid=7007030303355