# Real Analysis: Convergent Subsequence of Limit Superior

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.

© BrainMass Inc. brainmass.com October 10, 2019, 5:54 am ad1c9bdddfhttps://brainmass.com/math/real-analysis/real-analysis-convergent-subsequence-limit-superior-521342

#### Solution Summary

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

$2.19