1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

If a sum is 0, is the summand 0?

  1. Nov 30, 2014 #1
    Hey guys,

    Was just wondering something. Suppose I have an equation of the form


    how would I solve this? do I just set the summand = 0?
  2. jcsd
  3. Nov 30, 2014 #2


    Staff: Mentor

    No. If the terms in the sum can be positive or negative, their sum can be zero without any of them being zero. As a simple example, 2 + (-1) + (-1) = 0, but no single term equals zero.
    Last edited: Nov 30, 2014
  4. Nov 30, 2014 #3

    Stephen Tashi

    User Avatar
    Science Advisor

    What variables are you solving for? What symbols represent known values ?
  5. Nov 30, 2014 #4
    The real equation I'm dealing with is
    [itex]\sum_{i=1}^{n}\frac{1}{\sigma_{i}^{2}}2x(y_{i}-\alpha x -\beta x^{2})=0[/itex]

    and im trying to solve for alpha and beta but one at a time...
  6. Nov 30, 2014 #5

    Stephen Tashi

    User Avatar
    Science Advisor

    So it's "[itex] x [/itex]" instead of "[itex] x_i [/itex]"?`
  7. Nov 30, 2014 #6
    Yes I wrote it completely differently in the original post as I didnt think I would need to put the actual equation here but I changed my mind, sorry.

    There is no summation over [itex]x[/itex], only over the [itex]\sigma_{i}[/itex] and [itex]y_{i}[/itex].
  8. Nov 30, 2014 #7
    The closest I can get is

    [itex](\alpha x +\beta x^{2})\sum_{i=1}^{n}\frac{1}{\sigma_{i}^{2}}=\sum_{i=1}^{n}\frac{y_{i}}{\sigma_{i}^{2}}[/itex]

    No idea what to do from here
  9. Dec 1, 2014 #8

    Stephen Tashi

    User Avatar
    Science Advisor

    That equation doesn't have a unique solution. To get a unique solution, you need to know another equation involving [itex] \alpha [/itex] and [itex] \beta [/itex].

    Does this equation come from setting a partial derivative equal to zero? If so, perhaps there is another partial derivative that's supposed to be set equal to zero.
  10. Dec 1, 2014 #9
    Yes you are right - it turns out that the [itex]x[/itex] are also summed in addition to [itex]y_{i},\sigma_{i}[/itex], i had interpreted the situation inocorrectly.

    Everything is fine now thank you for your help! :D
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook