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    I have found out that even when the iteration is said to be convergent, some values in the series diverge...

    Why is it so?
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    (Original post by mystreet091234)
    I have found out that even when the iteration is said to be convergent, some values in the series diverge...

    Why is it so?
    Attachment 512737512733512700
    I think you're confusing the idea of convergence (where the sequence gets nearer and nearer to the end result) with monotone convergence (where the sequence gets nearer and nearer to the end result, but always approaching from the same direction). Contemplate the sequence  \frac{(-1)^n}{n}, contrasting with the sequence  \frac{1}{n} as n \rightarrow \infty.
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    (Original post by Gregorius)
    I think you're confusing the idea of convergence (where the sequence gets nearer and nearer to the end result) with monotone convergence (where the sequence gets nearer and nearer to the end result, but always approaching from the same direction). Contemplate the sequence  \frac{(-1)^n}{n}, contrasting with the sequence  \frac{1}{n} as n \rightarrow \infty.
    So in this example it is not monotone convergence, what is it then?

    Why you guys here know so many things:afraid:

    Thanks btw!
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    (Original post by mystreet091234)
    So in this example it is not monotone convergence, what is it then?
    Just ordinary bog-standard convergence! Given \epsilon > 0 one can find an N > 0 such that n > N \implies |a_n - a| < \epsilon

    Why you guys here know so many things:afraid:

    Thanks btw!
    Years of practice...
 
 
 
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