Explaining Convergent Sequences w/ Examples

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    Convergent Sequence
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SUMMARY

The discussion focuses on convergent sequences, specifically illustrating two examples. The first example, defined by the relation n+1 = n/2 + 1/n, converges to √2 as n approaches infinity. The second example, represented by the sequence {u_n} = (3n² - 1)/(n² - 5n), converges to 3. These examples demonstrate the behavior of convergent sequences in mathematical analysis.

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ctg81
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Could anyone please explain "convergent sequence" with example.
 
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Consider this
n+1=n/2+1/n and start from n=1. Find n+1 continuously from this relation and you will find that this sequence converges to sqrt(2)

Also the sequence
[tex] {u_n}=\frac{3n^2-1}{n^2-5n}[/tex]

converges to 3.

One can find many convergent sequences like this.
 

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