Question

WZON

請問第4題的第4小題？

21 江
3
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lo
第1章 極限與函數 3
4.
求下列各無窮數列的極限:
13
0 (1) lim
3" +2"
59
3 3" - 2n+1
(2) lim
n+ 3n+1 +21
(3) lim
-3n² tn
2n? +1
3n+4
(4) ( 11-31-6)-(1)
n-1
解
(2) n
()
(1)
3h+2
13"-2ht)
3h+ +
3 - 2.2²
3.3h + 2h
25
+
zh
5"
sh
5h
= ="
lim ( 23h + lim (2)
|- 2 )
3.1 + 6
hap
3 3
- oto
(2)
(4)
lim (-34th
hooo 2h²+1
-3th
- - lim
h00 2+1
h ha
-3
3
2
n-l
no 小
lim (3044
line 34
3th
- = lim

Answer 1

我就是我

平方差
(1-1/2²)(1-1/3²)...(1-1/n²)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3)...(1+1/n)(1-1/n)
=(3/2)(1/2)(4/3)(2/3)(5/4)(3/4)...((n+1)/n)((n-1)/n)
=(1/2)((n+1)/n)
=(n+1)/2n

極限為1/2

Answer 2

台大韓國瑜

a^2-b^2 = (a+b)(a-b)