hi,

i need to find the limit of the following sequence

lim (an)1/n

n®¥

where an the sequence defined recursively as follows

a1=1 and an+1=n(1-lnan) where ln is the natural logatithm

I can prove (using induction) that the sequence is increasing and not upper bounded but I don't know how to prove that. I'm sorry but I don't know how to write the sequence in the correct form, so I attached a doc file

lim (an)1/n=1 n®¥