Question

State whether the statement x_n (is not equal to) x_n-1 is always, sometimes or never true if x_n = f(x_n-1). Explain.

Answer 1

it is clearly not always true

Answer 2

why?

Answer 3

\(f\) can be any function right? so you could say \(f(x)=x+1\) and \(x_1=1\) so \(x_2=1+1=2\) and \(2\neq 1\)

Answer 4

ohhh. okay thanks

Answer 5

but it could be true, for example if \(f(x)=3\) and \(x_1=1\) then \(f(1)=3\) making \(x_2=3\) and also \(f(3)=3\) so \(x_3=3\) and so on

Answer 6

so sometimes but not always. okay thanks :)