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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 $\limsup$

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    Well, I would write a quite explicit formula for $x_n$ if I were you: surely you know the zeroes of the sine function, hence...2012-07-28
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    I haven't written anything down, but if I calculated this right in my head it seems the sequence $x_n$ converges, so lim sup is the limit.2012-07-29

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