對于數(shù)列{x
n},{y
n},其中y
n∈Z,對任意正整數(shù)n都有
,則稱數(shù)列{y
n}為數(shù)列{x
n}的“接近數(shù)列”.已知{b
n}為數(shù)列{a
n}的“接近數(shù)列”,且
.
(1)若
(n是正整數(shù)),求b
1,b
2,b
3,b
4的值;
(2)若
(n是正整數(shù)),是否存在k(k是正整數(shù)),使得A
k<B
k,如果存在,請求出k的最小值,如果不存在,請說明理由;
(3)若{a
n}為無窮等差數(shù)列,公差為d,求證:數(shù)列{b
n}為等差數(shù)列的充要條件是d∈Z.