飛航百科

標題:

數學題－－極限

發問:

若 lim [3^n/(n+2)!]=? n-->oo 請詳細解釋。

最佳解答:

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lim [3^n/(n+2)!]=? n-->oo 設a(n)=3^n/(n+2)! a(n+1)=3^(n_1)/(n+3)! So a(n+1)/a(n) =[3^(n+1)/(n+3)!]/[3^n/(n+2)!] =3^(n+1)/(n+3)!*(n+2)!/3^n =3/(n+3) since lim 3/(n+3)=0 n-->oo so lim [3^n/(n+2)!]=0 n-->oo

其他解答:

lim [3^n/(n+2)!] n-->oo =lim [(3/n+2)(3/n+1)(3/n)....(3/4)(3/3)(1/2)(1/1) n-->oo =0 SINCE =(3/n+2)(3/n+1)(3/n)...-->0 AS N-->oo AND ..(3/4)(3/3)(1/2)(1/1) IS CONSTANT