已知{a n }是由非负整数组成的无穷数列,该数列前n项的最大值记为A n ,第n项之后各项a n+1 ,a n+2 …的最小值记为B n ,d n =A n -B n . (Ⅰ)若{a n }为2,1,4,3,2,1,4,3…,是一个周期为4的数列(即对任意n∈N * ,a n+4 =a n ),写出d 1 ,d 2 ,d 3 ,d 4 的值; (Ⅱ)设d是非负整数,证明:d n =-d(n=1,2,3…)的充分必要条件为{a n }是公差为d的等差数列; (Ⅲ)证明:若a 1 =2,d n =1(n=1,2,3,…),则{a n }的项只能是1或者2,且有无穷多1.