A sequence is defined like the following $$x_1=1,$$ $$x_n=\sup\{x\in [0,x_{n-1}):\sin(1/x)=0\},n\ge 2$$ What is $\limsup x_n$?
I shall be highly obliged to those who will write the solution for me in detail.
Thank you, I am very weak in $\limsup$
A sequence is defined like the following $$x_1=1,$$ $$x_n=\sup\{x\in [0,x_{n-1}):\sin(1/x)=0\},n\ge 2$$ What is $\limsup x_n$?
I shall be highly obliged to those who will write the solution for me in detail.
Thank you, I am very weak in $\limsup$