# solve $\lim_{n \to \infty}\left( \frac{3+2n}{\sqrt{3}+\sqrt{2}n} + i\,n\right)$

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 Answer

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 $n$

-

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
show 1 more comment
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.8837646245956421, "perplexity_flag": "head"}