how to calculate "T"? analytically

[Sergey5318]

how to calculate "T"? analytically from:

\(\displaystyle \sum_{i=1}^{N}\left[ I_i \cdot e^{-\lambda_iT}\right] \ = \ 1\)

 

[Deleted member 4993]

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how to calculate "T"? analytically from:

\(\displaystyle \sum_{i=1}^{N}\left[ I_i \cdot e^{-\lambda_iT}\right]\)

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520​

Please share your work/thoughts about this problem.

 

[Sergey5318]

Thank you for correction this post.
i need to express "T" from this expression.
i do not have enough skills to do it.

 

[HallsofIvy]

Well, you can't! You would need some information about this expression such as a numerical value. You can "solve an equation" for a value of T but an expression is not an equation!

 

[Sergey5318]

Well, you can't! You would need some information about this expression such as a numerical value. You can "solve an equation" for a value of T but an expression is not an equation!

Thank you for reply.

this sum equal 1. so how can i get expression of "T"?

 

[Deleted member 4993]

Thank you for correction this post. i need to express "T" from this expression. i do not have enough skills to do it.

If you do not have enough skills to do it "completely" - you need to tell us "how far can you go?". At least tell us how would you start and think about continuing...

 

[Sergey5318]

I thought I could not see the simple way.
But if it's really difficult, I'd be grateful for a hint in which direction to think.

 

[Dr.Peterson]

View attachment 21512
how to calculate "T"? analytically from:

\(\displaystyle \sum_{i=1}^{N}\left[ I_i \cdot e^{-\lambda_iT}\right] \ = \ 1\)

Can you at least tell us what [MATH]I_i[/MATH] and [MATH]\lambda_i[/MATH] are? I don't think you can find T without knowing something about the other parts of the equation.

Or tell us the context of your question. If this is part of some bigger problem, we may need to know that.

 

[Sergey5318]

Ii and λi are usual variables without any special features

 

[JeffM]

Like Dr. Peterson, I greatly doubt that what you want to do is generally feasible. There might possibly be some special case where it is feasible. That is why he is trying to extract more information from you such as from what did you derive this monstrosity?

Obviously, the problem is trivial if N = 1. I doubt it is generally doable if N = 2, let alone any N > 1. I may be wrong. If you think you have a solution for N = 2, then the obvious next step is induction.

 

[Sergey5318]

the only thing I can add. T>0 and has only one value

 

[JeffM]

Well surely you can add the situation which gave rise to this equation. Perhaps there is a different way to analyze the underlying situation that provides a system of equations that can be solved for T.