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mercedesbenz
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Homework Statement
Please help me find examples.
[tex]u_n\subset [0,\infty)[/tex] and [tex]v_n\subset [0,\infty)[/tex] such that
[tex]u_{n+1}\leq u_n+v_n[/tex] for all n and [tex]\sum_{n=1}^{\infty}v_n[/tex]
is finite.
morphism said:Say you take u_n=0 for all n...
A sequence with finite sum is a sequence in which the terms eventually decrease and approach a specific value, resulting in a sum that is finite or finite in value. This means that the sequence has a finite or fixed number of terms, and the sum of those terms is a finite number.
Yes, an example of a un sequence with finite sum is the sequence 1, 1/2, 1/4, 1/8, 1/16, ... Each term in this sequence is half the value of the previous term, resulting in a finite sum of 2.
Yes, an example of a vn sequence with finite sum is the sequence 2, 4, 6, 8, 10, ... Each term in this sequence is 2 more than the previous term, resulting in a finite sum of 100.
Examples of un and vn sequences with finite sum can be used to better understand the concept of sequences with finite sum and to practice solving problems involving such sequences. These examples can also serve as a guide for creating your own sequences with finite sum for homework assignments.
Yes, some common mistakes to avoid when working with un and vn sequences with finite sum include not correctly identifying the pattern or rule of the sequence, not considering the specified number of terms in the sequence, and not paying attention to the signs of the terms (positive or negative). It is important to carefully analyze the problem and the sequence to avoid these mistakes.