I went through the proof of the question on this page: Prove $\limsup\limits_{n \to \infty} (a_n+b_n) \le \limsup\limits_{n \to \infty} a_n + \limsup\limits_{n \to \infty} b_n$ and it makes sense. I would just like to know that if an and bn have finite many terms would the proof still hold? Also if the proof holds please provide an example of strict inequality. Please pardon what is below I am using stackexchange for the first time so it isn't so neat. Let n ∈ of the Natural numbers, be defined on the interval [1,k] where ak is the final term of the sequence an. Likewise let q lie on this interval and bq is the final term of the sequence bn. Please prove that lim supn→k(an+bn)≤lim supn→k(an)+lim supn→q(bn), If the proposition is true then please provide an example of strict inequality.
2026-04-07 15:30:00.1775575800
limsup proof for finite sequences
60 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in REAL-ANALYSIS
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