Changing from Positive to Negative I may mess up a little bit...Sorry for that!
When we want a summation to go negative in case of odd numbers and positive otherwise , we use:
$$\sum\limits_{i=1}^{12} \color{red}{{(-1)}^i} 2x^3 $$
But what if I want it to go positive for say $i=1$ to $i=8$ and then turn negative Without using:
$$\sum\limits_{i=1}^{8} 2x^3 \space + \space \sum\limits_{i=9}^{12} -2x^3$$

I mean i want to use the condition in just one summation instead of splitting things up...Then what to do?
$$\sum\limits_{i=1}^{12} {(-1)}^{\color{blue}{?}} 2x^3$$

Thanks a lot!

You could use the sign function but you would want to make sure it doesn't land on zero
so in your case
$$ \DeclareMathOperator{\sign}{sgn} \sum_{i=1}{\sign(17-2i)2x^3} $$
$$ \DeclareMathOperator{\sign}{sgn}
\sign(x) = \left\{\begin{matrix}
-1 & x<0 \\ 
 0& x=0 \\ 
 1& x>0 
\end{matrix}\right. $$
$$\DeclareMathOperator{\sign}{sign} $$
