![]() ![]() Is bounded above at ?a_n\le 7/2? and bounded below at ?a_n>1/3?. Remember, we calculated this answer by taking the limit of our sequence as it approaches infinity, so our sequence will be greater then the bounded limit but not equal to it. This subsequence is not necessarily contiguous or unique. In less formal terms, a sequence is a set with an order in the sense that there is a first element, second element and so on. In this case our sequence is bounded below at ?a_n>1/3?. In computer science, the longest increasing subsequence problem aims to find a subsequence of a given sequence in which the subsequences elements are sorted in an ascending order and in which the subsequence is as long as possible. Since we got a real answer for our limit, we know our sequence is also bounded below. The smallest value of an increasing monotonic sequence will be its first term, where ?n=1?. Each member of a monotone increasing sequence is greater than or equal to the preceding member each member of a monotone decreasing sequence is less than or. Asking for solutions without any effort on your part, is not okay.Bounded above by the largest value of the sequenceÄ«ounded below by the smallest value of the sequence Beginner questions and asking for help with homework is okay. Post your question and outline the steps you've taken to solve the problem on your own. In a convergent sequence, the individual terms of the sequence approach zero. ![]() A divergent sequence is an infinite sequence that is not convergent, meaning that the infinite sequence of the partial sums of its series does not have a finite limit. Do not use ChatGPT in a question or an answerÄon't just post a question and say "HELP". Divergence is a concept employed in the context of limits, sequences, and series.Do not solicit or offer payments to complete your assignments or tests.No cheating - do not post questions from exams, tests, midterms, etc.If An: n N A n: n N is monotone non-increasing, then its limit is. No post flooding - Limit your posts to 2 or 3 questions a day The down- and up-arrows imply the monotonicity of the sequence the A A is the actual limit, which is the intersection for a non-increasing sequence and the union for a non-decreasing sequence.Don't be a jerk - don't be obnoxious or rude.Homework policy - asking for help is okay, asking to be given the solution is not.Make your question clear and concise - include steps you have tried.Stay on topic - this subreddit is for math questions no how-to guides, or non math related questions.Explain your post - show your efforts and explain what you are specifically confused with. Probability measure is continuous along monotone sequences of events. ![]()
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