Question

Give precise mathematical definitions or descriptions of each of the concepts that follow. Then illustrate the definition or description with a graph or an algebraic example.

The limit of a sequence.

Short answer

The limit of a sequence is the value the sequence approaches as the number of terms goes to infinity. For example,$\underset{n\to \infty }{lim}\frac{n-1}{n+1}=1$

Step-by-step solution

Step 1. Given Information   

The given statement is the limit of a sequence.

Step 2. Explanation  

The limit of a sequence is the value the sequence approaches as the number of terms goes to infinity.

The number L is the limit of the sequence $a_n\mathrm{if}\mathrm{given}\epsilon >0,a_n\approx L\mathrm{for}n>>1$

If such an L exists, we say the sequence is convergent otherwise the sequence is divergent.

For example, $\underset{n\to \infty }{lim}\frac{n-1}{n+1}=1$, in this the function is approaching limit equals to 1 as n increases.