[高微] 一題高微
Xn→Xo
→lim (X1+....+Xn)/n
n→∞ =Xo
Evaluate lim (1+2√2+.....+n√n)/n
n→∞ =?
sol:Xn= n√n , lim Xn
n→∞ =1
∴ lim (1+2√2+.....+n√n)/n
n→∞ =1
問題:為什麼Xn=n√n,lim Xn 會等於一啊??
n→∞
謝謝
自問自答:lim Xn
n→∞ = A
兩邊取ln→lim ln(n)/n
n→∞ =ln(A)
L'Hospital→lim 1/n
n→∞ = 0 =ln(A)
兩邊取e → e^0 = e^[ln(A)] → 1 = A
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※ 編輯: TampaBayRays 來自: 114.43.144.76 (11/27 20:49)