Answer by Yiorgos S. Smyrlis for Prove a given sequence of real numbers is...
It is consequence of the following:If a sequence is monotonic and bounded, then it converges.
View ArticleAnswer by John for Prove a given sequence of real numbers is convergent
To show that $y_n$ is convergent, focus on the properties of $y_n$. There are several facts about $y_n$ that you should be able to deduce directly from your above statements. Do those facts help you to...
View ArticleProve a given sequence of real numbers is convergent
Given the sequence of real numbers $\{x_n\}_{n \in \mathbb N}$, we define $\{y_n\}_{n \in \mathbb N}$ where $y_n=\max\{|x_1|,...,|x_n|\}$ for each $n \in \mathbb N$. Prove that if $\{x_n\}_{n \in...
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