i have a sequence which is defined by the following:

a(1) ∈ (0, 0.5)

a(n+1) = a(n) - 0.5a(n)^(n+1)

1: Is it possible to form the ''equation'' of the sequence a(n) with the above conditions? if yes, how?

2: with n -> infinite, is it possible to find a limit? Aren't there more than one possibilities?

sorry for the fuzz..