Re: [考古] 請問三題計算題
※ 引述《flygey (努力達成目標)》之銘言：
: 3.Sequence{an} whose the first three term are:
: n=1
: a1=1+1/2 , a2=1+1/(2+1/2) , a3=1+1/[2+1/(2+1/2)]
: (1)what is the fifth term?
: (2)Give the general form of an
: (3)Is the sequence {an} convergence or divergence ? If convergence then
: find it's limit else state the reason for divergence
我把昨天沒有補好的convergence證明補好
a_n = a_1 + (a_2-a_1) + ......
= a_1 + b_1 + b_2 + ......
= a_1 + sigma[b_n]
for b_n = a_(n+1) - a_n
由題目a_n本身的表達方式可以知道b_n是正負正負的交錯級數
│b_n│=│(2-a_n^2)/(1+a_n)│
│b_(n-1)│=│(2-a_n^2)/[(a_n)-1]│
│b_n│ │[(a_n)-1]│
=>------------ = ------------- < 1 (a_n >1)
│b_(n-1)│ │1+a_n│
=>sigman[b_n] is convergent
=>sequence is convergent
: 這題也是不知該用什麼公式算
: 感謝版友指導解題
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