I can't figure out what I'm doing wrong here:
Table[Nest[# + 0.1 * -i * #^2 &, 2, 1] , {i, 0, 0.5, 0.1}]
(* {2., 1.96, 1.92, 1.88, 1.84, 1.8} *)
The problem is that it keeps using 2 in the argument instead of the last result. Normally the first parameter is the starting point, when using the pure function.
The output should be something like
(* {2., 1.96, 1.883, 1.777, 1.651, 1.514} *)