Given is the following sequence $a_n:= (-1)^n*(\frac{241216}{n}+1)$ and I have to find two convergent subsequences with different limits. At first I thought of $a_{n_1}:= (-1)^{2n}*(\frac{241216}{2n}+1)$ and $a_{n_2}:= (-1)^{2n-1}*(\frac{241216}{2n-1}+1)$ so the two subsequences for n odd and even. But both seem to diverge.
two convergent subsequences
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convergence
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0Remember that these are sequences rather than series. For your first one, the fraction-term goes to 0, leaving a limit of $1$. – 2017-01-08
1 Answers
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You idea is good: in those two cases you get
$$\pm\left(\frac{241216}n+1\right)\xrightarrow[n\to\infty]{}\pm1$$
depending on whether you took even or odd indexes, resp.