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## Homework Statement

I have to find all the partial limits {I hope this is how this term named in English} of a sequences

## Homework Equations

[tex]a_1=0[/tex]

[tex]a_{2n}=\frac {a_{2n-1}} {3}[/tex]

[tex] a_{2n+1} = 1/3 + a_{2n}[/tex]

## The Attempt at a Solution

I have tried to prove first that sequences of all the even terms converges due to fact that sequence is monotonic and have a suprimum, but have failed to prove it.

Another problem is that subsequences of odd term is non monotonic, but I also can't use the Cantor's Lemma.

Could you please suggest how to approach this problem?

Thanks.

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