- #1
transgalactic
- 1,395
- 0
[tex]a_1=\sin x [/tex]
[tex]-\infty<x<\infty[/tex]
[tex]a_{n+1}=\sin a_n [/tex]
prove that [tex]a_n[/tex] convergent and find
[tex]\lim _{n->\infty}a_n=?[/tex]
the solution that i saw is that because
[tex]a_1=\sin x [/tex] then its bounded from 1 to -1
so
|[tex]a_{n+1}[/tex]|<|[tex]\sin a_n[/tex]|=<|[tex]a_n[/tex]|
so its non increasing and it goes to 0.
but the teacher says that its not a proof
why its not a proof
how to solve it correctly??
[tex]-\infty<x<\infty[/tex]
[tex]a_{n+1}=\sin a_n [/tex]
prove that [tex]a_n[/tex] convergent and find
[tex]\lim _{n->\infty}a_n=?[/tex]
the solution that i saw is that because
[tex]a_1=\sin x [/tex] then its bounded from 1 to -1
so
|[tex]a_{n+1}[/tex]|<|[tex]\sin a_n[/tex]|=<|[tex]a_n[/tex]|
so its non increasing and it goes to 0.
but the teacher says that its not a proof
why its not a proof
how to solve it correctly??