Can someone Explain Newton's Sums to me?

The explanation,Some examples and a few exercise Problems would be really appreciated.

Thanks in advance.

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## Comments

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TopNewestSorry, not at home. Answering from mobile (difficult to type). Will be home in 2-3 days. Will surely help you then.

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When's your vacation going to be over ?

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I 'll be at home on 25th. And my School.starts on 1st April.

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Do you still need help ?

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Yeah... Newton sums are still going over my head, although I understood like 20% of it XD

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Start solving questions :)

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Ok. Where do you have a doubt ?

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$P_n$ means (For a quadratic polynomial) that $P_n = a^n + b^n$ where $(a,b)$ are roots of Polynomial $f(x)$

Any other Problem ?

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@Prasun Biswas @Calvin Lin @Rajdeep Dhingra @Azhaghu Roopesh M Please help.. :/

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Well, it'd be better if you could point out the parts you don't understand in the Brilliant wiki on Newton's sums.

Also, I'd recommend the Wikipedia article on Newton's Identities. I learnt it from there. :D

There are two points to note when learning Newton's Identities. It is a method that helps you to form a recurrence for power sums of roots, so it'd be better if you have a good understanding of recurrence relations. Also, applications of Newton's Identities mostly use Vieta's formulas because you need to find the elementary symmetric polynomials first before calculating the power sums. If you get confused with "too many formulas" there, just remember the concise form stated in the Brilliant wiki under the section "General Form".

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I have learnt all the Vietas formulae but Ill start working on the Recurrence relations right away...

Wah wah!! XD

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Have you tried the Brilliant wiki on it ?

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Yeah.. I didn't learn much. The wiki must be good though it went over my head.

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Then try the AoPS wiki on Newton's Sums . I had learnt it from there since when I had learnt it , the wiki on Brilliant wasn't filled out . Or you can always download some pdfs on the topic . Now that always works (for me atleast!)

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Check out the Brilliant wiki - Newton's Identities, which is in the Vieta formula chapter in algebra.

Thanks to @Prasun Biswas for contributing this article :)

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Sir, I did go through to the wiki but it went over my head. Can someone please explain it in an easier fashion?

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