收敛数列的有界性问题设数列{Xn}有界,又lim Yn=0,证明:lim XnYn=0.囧么办?111
问题描述:
收敛数列的有界性问题
设数列{Xn}有界,又lim Yn=0,证明:lim XnYn=0.囧么办?111
答
|xn|≤M
-Myn≤xn.yn≤Myn
-Mlim(n->∞)yn≤lim(n->∞)xn.yn≤Mlim(n->∞)yn
0 ≤lim(n->∞)xn.yn≤0
=>lim(n->∞)xn.yn =0