Since we want to find the lower bond and the sequence is decreasing, we will put the limits to infinity.Īs the sequence is increasing, is a lower bound and the infimum. To find the infimum or lower bound, we have two methods. Study the following sequences and determine if they are bounded.Īs the sequence is decreasing, 3 is an upper bound and the supremum. Therefore, all the terms in the sequence are between k and K'. The smallest upper bound is called the supremum.Ī sequence is bounded if it is bounded above and below, that is to say, if there is a number, k, less than or equal to all the terms of sequence and another number, K', greater than or equal to all the terms of the sequence. The greatest lower bound is called the infimum.Ī sequence is bounded above if all its terms are less than or equal to a number K', which is called the upper bound of the sequence. step-by-step solution of limits along with a plot and series expansion. Bounded BelowĪ sequence is bounded below if all its terms are greater than or equal to a number, K, which is called the lower bound of the sequence. Limit solver solves the limits using limit rules with step by step calculation. One of them is Bounded Below and other is the Bounded Above. A bounded sequence can be either positive or negative, how you are going to find out? That is why mathematicians categorized the bounded sequence into two types. Now you know that when we are talking about the bounded sequence, we are talking about the monotonic sequence. The positive end is increasing at some rate which mean that it has a bound. For the case of, let's construct the results.Īs you can note that the numerator is increasing by and denominator is increasing by, hence we can conclude that the series is increasing. This is because the amount which the series is growing on the positive end is equal to the amount that is decreasing on the negative end. These types of series have no upper limit neither lower limit. Let's talk about and construct the results for different values of n. To better understanding, we got two sequences for you.
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