The numerical sequence is presented by function of a look an=f(n) which is set on a set of natural numbers. In most cases in the numerical sequences of f(n) it is replaced with an. Numbers of a1, a2, …, an – members of the sequence, and a1 – the first, a2 – the second, ak – k-y. On the basis of data of function of the numerical sequence the schedule is under construction.
It is required to you
- - reference book on mathematics;
- - ruler;
- - notebook;
- - simple pencil;
- - basic data.
Instruction
1. Before starting creation of the schedule of the sequence, define what function is the numerical sequence. Distinguish not increasing or nondecreasing sequence (an) for which at any value n inequality of a look is fair: an≥an+1 or an≤an+1. Provided that an> an+1 or an
2. At creation of the schedule of the numerical sequence pay attention that the sequence (an) can be limited from below or from above: for this purpose there has to be number M that at any value n there was fair inequality of anM or anM. Moreover, the schedule of the numerical sequence can be limited along with two parties: such sequence is called limited.
3. Construct the schedule of the numerical sequence in which and - a sequence limit (for the set each small positive number ε such number N which at n> N satisfied to value of inequality |xn-a| has to be found