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Chapter 7: Q. 6 (page 655)

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

Expert verified

The limit of a sequence is the value the sequence approaches as the number of terms goes to infinity. For example,limn鈫�鈭�n-1n+1=1

Step by step solution

01

Step 1. Given Information   

The given statement is the limit of a sequence.

02

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 anifgiven蔚>0,an鈮�Lforn>>1

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

For example, limn鈫�鈭�n-1n+1=1, in this the function is approaching limit equals to 1 as n increases.

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