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szg07

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I have been solving some problems in physics and mathematics that often involve expressions where you need to represent the sum of products,

a simple example would be :

resistors in parallel

when 3 resistors are in parallel, you always get an expression like :

(R1*R2*R3)/ (R1*R2 + R1*R3 + R2*R3)

and when you have an n resistors in parallel, that would give :

(R1*R2*R3*...*Rn) / (the sum of all combinations of (n-1) resistors out of n resistors)

my problem is that I would like to be able to represent such results with a general formula

using the SIGMA sign or PI sign whatever the number of resistors involved

and even with matrices (determinant)

How would I do that?

Hope you can help me!

Thanks a lot