Convergent sequence

[jessebu]

Here's the question:
Suppose that f is continuous and that the sequence x, f(x), f(f(x)), ... converges to c. Prove that c is a "fixed point." (i.e. that f(c) = c).

I'm not quite sure what this question is asking, so any help as to what it means would be great.

 

[daon]

Are you assuming this is true for all x?

 

[jessebu]

yeah, i guess so.
the question doesn't specify but thats what i would assume