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February 27th, 2018, 02:46 AM   #1
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Proof by induction

Hello,

I found this interesting result and I wanted to demonstrate it through induction:

https://ibb.co/fdYjfx

where the sigmas are symmetric functions (it's described in the picture, and apologies for it being in French).

The result is true for each x1, x2, ..., xn in the sets of the reals or of the complex numbers.

For n = 1, no issue arises, however it is the next step which appears quite tricky to me. I tried to use the induction hypothesis by splitting the product, but to no avail. Could I have some ideas?

Best regards.

(Apologies if this is the wrong board)
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February 27th, 2018, 03:24 AM   #2
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This seems to be the same result in English.
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February 27th, 2018, 12:09 PM   #3
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Thanks skipjack, do you - by any chance - have an idea for induction?
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