Monday, 1 February 2016

sequences and series - an+1=log(1+an), a1>0. Then find limnrightarrowinftyncdotan


Suppose that an+1=log(1+an), a1>0. Then find lim.




I can find \lim_{n \rightarrow \infty}a_n=0. But I have no idea how to find \lim_{n \rightarrow \infty} n\cdot a_n. (In this problem, \log denotes the natural logarithm.)
Could you give me key idea about solving this problem?

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