Given is the complex sequence:
$$(a_n)_{n\epsilon \Bbb N} \subset \Bbb C $$ with the subsequences:
$$a_n = 5i^n(1+{1\over n^3})$$
How do I find 5 another subsequences of $$(a_n)_{n\epsilon \Bbb N} $$ with different limits each?
2026-04-02 13:55:28.1775138128
Subsequences with different limits
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If I understand well, the sequence $(a_n)$ is given by $a_n=5i^n\left(1+\dfrac{1}{n^3}\right)$. So, $(a_{4n}),(a_{4n+1}),(a_{4n+2}),(a_{4n+3})$ are four subsequences with pairwise distinct limits. I am afraid that $\pm 5, \pm 5i$ are all possible limits of subsequences of this sequence. Indeed, all terms ot our sequence are located on the positive (negative) halfline of real (imaginary) numbers.