The discussion revolves around the mathematical question of whether a summand must be zero if the sum of several terms equals zero. Participants explore a specific equation involving summation and variables, seeking to understand how to approach solving it, particularly in relation to the values of certain parameters.
Participants generally agree on the idea that a sum can be zero without all summands being zero, but there is no consensus on the specifics of solving the equations presented, as multiple approaches and interpretations are discussed.
Some limitations include the need for additional equations to achieve unique solutions for the parameters alpha and beta, as well as the dependence on the interpretation of the variables involved in the summation.
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.Dixanadu said:Hey guys,
Was just wondering something. Suppose I have an equation of the form
[itex]\sum_{i=0}^{n}\frac{1}{x_{i}}(a-by_{i})=0[/itex],
how would I solve this? do I just set the summand = 0?
What variables are you solving for? What symbols represent known values ?Dixanadu said:how would I solve this?
Dixanadu said: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]
Dixanadu said: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