0
$\begingroup$

The question asks me to justify if the complex series converges absolutely, which leads me to think that I should use the comparison test (instead of the root or ratio tests), the series itself is sum from n=1 to infinity of $$1/(n^2+i)$$ But I'm not sure how to find another series to compare it to now that it is complex? Thanks!

$\endgroup$
1
$\begingroup$

Hint: $$ |n^2+i|\geq|n^2|-|i|= n^2-1 . $$

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ But in order to prove convergence don't I need to find something larger than the series? $\endgroup$ – Agnes Oct 9 '16 at 18:16
  • $\begingroup$ If $a\ge b$ then $1/a\le 1/b$. $\endgroup$ – Julián Aguirre Oct 9 '16 at 18:27
  • $\begingroup$ Actually $|n^2+i| > n^2.$ $\endgroup$ – zhw. Oct 10 '16 at 17:34

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.