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    Real Analysis: Convergent Subsequence of Limit Superior

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    Suppose the lim (subscript n --> infinity) sup a_n = theta is finite. Prove there exists a subsequence that converges to theta. Please view the attachment to see the full question, including necessary symbols.

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    Solution Summary

    The triangle inequality is used to show that if a sequence has a finite limit superior, it must have a convergent subsequence.