The 'recursive relation' defining the sequence can be written as...

(1)

The behavior of the sequence depends from the 'initial value' and from the parameter . We have three possibilities...

a) . In this case any will produce a sequence that tends to , any a sequence that tends to and the 'all zeroes sequence'...

b) . In this case any will produce a sequence that tends to , any a sequence that tends to and any a sequence that tends to 0...

c) . In this case any will produce a sequence that tends to , any a sequence that tends to , any an 'oscillating sequence' and the 'all zeroes sequence'...

Kind regards