下列哪些無窮數列為收斂數列?
(A) <6> (B)<3乘(-1^n)> (C)<(7n^2+17^100)/(3n^2-1)> (D)<3^2n/5^n> (E)<logN/2^N>
答案是ACE
A是定值所以為收斂? C上下都除以n^2 定值為7/3,也是收斂? D不也是定值9/5嗎 怎麼不是收斂數列?
高中數學（收斂數列）?
2017-05-14 5:22 pm
回答 (1)
2017-05-14 5:33 pm
下列哪些無窮數列為收斂數列?
(A) <6> (B)<3乘(-1^n)> (C)<(7n^2+17^100)/(3n^2-1)> (D)<3^2n/5^n> (E)<logN/2^N>
Sol
(A)
lim(n->∞)_a(n)=6
A正確
(B)
lim(n->∞)_a(2n)=3
lim(n->∞)_a(2n+1)=-3
B錯誤
(C)
lim(n->∞)_(7n^2+17^100)/(3n^2+1)=7/3
C正確
(D)
lim(n->∞)_3^(2n)/5^n
= lim(n->∞)_(9/5)^n
9/5=1.8>1 =>diverge
D錯誤
(E)
lim(n->∞)_ logn/2^n
=0
E正確
(A) <6> (B)<3乘(-1^n)> (C)<(7n^2+17^100)/(3n^2-1)> (D)<3^2n/5^n> (E)<logN/2^N>
Sol
(A)
lim(n->∞)_a(n)=6
A正確
(B)
lim(n->∞)_a(2n)=3
lim(n->∞)_a(2n+1)=-3
B錯誤
(C)
lim(n->∞)_(7n^2+17^100)/(3n^2+1)=7/3
C正確
(D)
lim(n->∞)_3^(2n)/5^n
= lim(n->∞)_(9/5)^n
9/5=1.8>1 =>diverge
D錯誤
(E)
lim(n->∞)_ logn/2^n
=0
E正確
收錄日期: 2021-04-30 22:14:04
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20170514092233AAmQIez