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ppy

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## Homework Statement

2.11. Determine (explicitly) a convergent subsequence of the sequence in R2 given for n =

1; 2; : : : by

xn =(e[itex]^{n}[/itex]sin(n[itex]\pi[/itex]/7),((4n+3/3n+4)cos(n[itex]\pi[/itex]/3))

I know that the Bolzano-weierstrass theorem says that every bounded sequence has a convergent subsequence. I thought I should first check that the xn is bounded by checking each individual co-ordinate. however isn't x[itex]_{n,1}[/itex] not bounded? Therefore surely x[itex]_{n}[/itex] cannot have a convergent subsequence? as doesn't it just go to infinity? Help needed urgently!!

Thanks