（Ⅰ）∵数列{an}满足a1=1，an+1=2n+1anan+2n （n∈N*），∴2n+1an+1＝2nan+1，即2n+1an+1−2nan＝1，∴数列{2nan}是公差为1的等差数列．（Ⅱ）由（Ⅰ）可得2nan＝2a1+n−1=n+1，∴an＝2nn+1．（Ⅲ）由（Ⅱ）知，bn=...