Working definition of limit - sequences and series, Mathematics

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Working Definition of Limit

1. We state that

2433_Working Definition of Limit - sequences and series 1.png

if we can create an as close to L like we want for all adequately large n.  Alternatively, the value of the an's approach L because n approaches infinity.

2. We define that

1591_Working Definition of Limit - sequences and series 2.png

Determine if we can make an as large as we wish for all sufficiently large n.  Once again, alternatively, the value of the an's get larger and larger withno bound as n approaches infinity.

3.   We define that

2421_Working Definition of Limit - sequences and series 3.png

Whether, we can make an as large and negative as we wish for all sufficiently large n.  Once again, in other words, the value of the an's are negative and obtain larger and larger without bound because n approaches infinity.


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