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I want an alternating series formula that generates three negatives and three positives together.I know that we can do the same except that it is two negative and three positive can performed by triangle numbers.(See the link below.But I cannot find anything that generates three negative and three positive.For this we should do three odd and three even series and then put it in the power of $-1$.

Recommended:How to create alternating series with happening every two terms

update1:The series:${1,1,1,-1,-1,-1,1,1,1,-1,-1,-1,...}$

update2:We didn't learned floor function or trigonometry yet.

Community
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Taha Akbari
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    What on earth does "an alternating series formula that generates three negatives and three positives together" mean? Or for that matter, what does "with happening every three terms" mean? "Happening"??? – hmakholm left over Monica Jun 25 '16 at 16:10
  • Since the OP updated the series in need, now the question seems clear, especially analogous to the linked question in the question body. So I nominate to reopen it. – awllower Jun 26 '16 at 06:38

2 Answers2

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Hint

$$(-1)^{\lfloor \frac{n}{3} \rfloor}$$ gives you alternately 3 pluses and 3 minuses. If you add $+1$ at the top you can start with 3 minuses

N. S.
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Are you looking for a function $f(n)$ that generates 3+,3-,3-,3+,...? What about

$$ f(n) = sign\left(\sin (\pi/6 + n\pi/3) \right) $$

Edit: if you don't like the sign function, you can replace it with its expression, and obtain

$$ f(n) = \frac{\sin (\pi/6 + n\pi/3)}{|\sin (\pi/6 + n\pi/3)|} $$

bartgol
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  • We haven't learned $90$% of what you used. – Taha Akbari Jun 25 '16 at 16:14
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    You haven't learned sine and cosine but you are already learning sequences and series? If it's the sign function that bothers you, see the edit. – bartgol Jun 25 '16 at 16:15
  • Yes we didn't learned $sin$ and $cos$ yet. – Taha Akbari Jun 25 '16 at 16:16
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    What functions are we allowed to use here? No sin/cos, no integral part... Give us some idea of what we can use. – bartgol Jun 25 '16 at 16:18
  • I think we should use sth like triangle numbers because it is our main subject but anyway+1 – Taha Akbari Jun 25 '16 at 16:20
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    If you people haven't yet studied trigonometric function it is then worrying that you're attempting to deal with infinite series...And you did tag your question "calculus", "series"...and even "power series"!, etc. – DonAntonio Jun 25 '16 at 16:24
  • I agree with Joanpemo. I think what you are really asking is "I need a function $g(n)$ that alternates 3 odds and 3 evens in a row". Given such function, your answer would be $(-1)^{g(n)}$. But then your tag should be more something like elementary number theory, not calculus or series... – bartgol Jun 25 '16 at 16:26
  • Yes you are right.Done. – Taha Akbari Jun 25 '16 at 16:28