## anonymous one year ago How to solve this type of sequence? 1)The sequence given is: 〖(a_n)〗_(n ϵ N) , such as: a_1= 1/3 for every n ϵ N , a_(n+1)=(2n+1)/(4n+3) a_n. Find a_3 ? Considering the fact that every monotone decreasing and bounded in sequence is a convergent sequence, show that the sequence 〖(a_n)〗_(n ϵ N) is a convergent sequence. Find lim┬(n→∞)⁡〖a_n 〗

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1. Loser66

Why do you go to a complicated way? just plug n =1,2 into the given equation and you get \(a_3\)

2. Loser66

\(a_{n+1}= \dfrac{2n+1}{(4n+3)a_n}\) If n =1, then \(a_{n+1}= a_{1+1}= a_2 =\dfrac{2*1+1}{(4*1+3)a_1}\)

3. Loser66

repeat with n =2, you get a3