0
$\begingroup$

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

1 Answers 1

1

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 $n$

  • 0
    why it doesnot depend on $n$, i dont get the point2012-12-15
  • 0
    you're right, I should start avoiding this kind of words, they do not carry any positive contribution and can lead to awkward moments!2012-12-15
  • 0
    @doniyor You did not give any information about what $i$ is. In principle it could be something like $-n$ or $-e^n$!2012-12-15
  • 0
    ok then if $i$ is the imaginary unit the sequence diverges in modulus as you said!2012-12-15
  • 0
    it means that the sequence of the absolute values of the terms of your sequence goes to +infinity!2012-12-15
  • 0
    okay, fine! :) Thanks dude. great help!2012-12-15