即xn?1?xn?...?x2?M。于是
xn?1?xn?xn?xn?1?...?x2?x1
?xn?1?2xn?2xn?1?...?2x2?2x1?2M?x1
所以数列?xn?是B-数列。
（III）若数列?an? {bn}是B?数列，则存在正数M1.M2，对任意的n?N?,有 an?1?an?an?an?1?....?a2?a?1M
1bn?1?bn?bn?an?1?....?b2?b1?M2
注意到an?an?an?1?an?1?an?2?...?a2?a1?a1 ?an?an?1?an?1?an?2?...?a?2a?1a?1M?a1 同理：bn?M2?b1w.w.w.k.s.5.u.c.o.m 1
记K2?M2?b2，则有K2?M2?b2
an?1bn?1?anbn?an?1bn?1?anbn?1?anbn?1?anbn
?bn?1an?1?an?anbn?1?bn?K1an?1?an?k1bn?1?bn
因此 K1(bn?1?bn?b?n?n1b?......?a21a?)2k?M1 1kM2 +K1(bn?1?bn?bn?bn?1?......a2?a1)?k2M1?k1M2 故数列anbn是B?数列
??w.w.w.k.s.5.u.c.o.m