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I am checking this sequence for convergence but i am not sure whether i am on the right path in calculations, these steps are what i am doing now. $\infty + n$ will go to infinity, right?

$$\lim_{n \to \infty} \frac{3+2n}{\sqrt{3}+\sqrt{2}n} + i\,n = \lim_{n \to \infty} \frac{3+2n}{\sqrt{3}+\sqrt{2}n} + \lim_{n \to \infty}i\,n = \sqrt{2} + \infty = \infty$$

am i okay? can someone please correct me if i am wrong. many thanks for any guidance

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1 Answer 1

up vote 1 down vote accepted

If $i$ the imaginary unit then the sequece diverges in modulus.

That sequence will diverge in any case if $i\not = -\sqrt{2}$ is a constant and does not depend on $n$

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why it doesnot depend on $n$, i dont get the point –  doniyor Dec 15 '12 at 15:26
    
you're right, I should start avoiding this kind of words, they do not carry any positive contribution and can lead to awkward moments! –  Moritzplatz Dec 15 '12 at 15:27
    
@doniyor You did not give any information about what $i$ is. In principle it could be something like $-n$ or $-e^n$! –  Moritzplatz Dec 15 '12 at 15:29
    
ok then if $i$ is the imaginary unit the sequence diverges in modulus as you said! –  Moritzplatz Dec 15 '12 at 15:33
    
it means that the sequence of the absolute values of the terms of your sequence goes to +infinity! –  Moritzplatz Dec 15 '12 at 15:40

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