Having sequence like $$ \beta_1 \cos\theta_1 + \beta_2 \cos\theta_2 + \beta_3 \cos\theta_3 + \dots + \beta_n \cos\theta_n$$ it is possible to present it using summation notation as follows:

$$ \sum_{i=1}^n \beta_i \cos\theta_i $$

But is it correct to present a sequence like

$$ \beta_1 \cos\theta_1 + \beta_2 \cos\theta_2 - \beta_3 \cos\theta_3 \pm \dots \pm \beta_n \cos\theta_n$$ as summation when a particular elements may need to be used with a negative sign?

Update 1

Unfortunately there is no any pattern for + and -. The sign is deduced by manually interpreting the contour of a polygon.

Update 2

Also, Is it correct for integration notation?

  • 2
    $\begingroup$ You can do it, but it may not be pretty. Is there some easy pattern to the $+$ and $-$s? Do they alternate? Are they two and two? Some other pattern? $\endgroup$ – Arturo Magidin Mar 2 '12 at 21:06
  • 3
    $\begingroup$ A commonly used, but not necessarily attractive way is to write $\sum \epsilon_i \beta_i \cos\theta_i$, where each $\epsilon_i$ is $1$ or $-1$. $\endgroup$ – André Nicolas Mar 2 '12 at 21:21
  • $\begingroup$ If the signs alternate, you can write $\sum_{i=1}^{n}(-1)^{i+1}\beta_i\cos\theta_i$ or $\sum_{i=1}^{n}(-1)^i\beta_i\cos\theta_i$. $\endgroup$ – wjm Mar 2 '12 at 22:35
  • 1
    $\begingroup$ Is what correct for integration notation? You haven't given any integration notation. $\endgroup$ – Gerry Myerson Mar 3 '12 at 4:05

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