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Can someone Explain Newton's Sums to me?

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

Thanks in advance.

Note by Mehul Arora
2 years, 2 months ago

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Do you still need help ? Rajdeep Dhingra · 2 years, 2 months ago

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@Rajdeep Dhingra Yeah... Newton sums are still going over my head, although I understood like 20% of it XD Mehul Arora · 2 years, 2 months ago

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@Mehul Arora Ok. Where do you have a doubt ? Rajdeep Dhingra · 2 years, 2 months ago

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@Rajdeep Dhingra Like I'm trying but kinda not understanding the terminology basically.. Like ini the Brilliant wiki, What is P1? etc... Maybe if I can understand the terminology Ill be able to comprehend it. Mehul Arora · 2 years, 2 months ago

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@Mehul Arora \(P_n\) means (For a quadratic polynomial) that \( P_n = a^n + b^n \) where \( (a,b)\) are roots of Polynomial \(f(x)\)
Any other Problem ? Rajdeep Dhingra · 2 years, 2 months ago

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@Mehul Arora Start solving questions :) Azhaghu Roopesh M · 2 years, 2 months ago

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@Azhaghu Roopesh M Yeah.. I am trying. Just learnt Vieta's. Trying to perfect it. :) Mehul Arora · 2 years, 2 months ago

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@Mehul Arora Best of luck :) Azhaghu Roopesh M · 2 years, 2 months ago

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@Azhaghu Roopesh M Thanks!! Mehul Arora · 2 years, 2 months ago

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Sorry, not at home. Answering from mobile (difficult to type). Will be home in 2-3 days. Will surely help you then. Rajdeep Dhingra · 2 years, 2 months ago

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@Rajdeep Dhingra When's your vacation going to be over ? Azhaghu Roopesh M · 2 years, 2 months ago

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@Azhaghu Roopesh M I 'll be at home on 25th. And my School.starts on 1st April. Rajdeep Dhingra · 2 years, 2 months ago

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@Rajdeep Dhingra Ok. Enjoy :) Azhaghu Roopesh M · 2 years, 2 months ago

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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 :) Calvin Lin Staff · 2 years, 2 months ago

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@Calvin Lin Sir, I did go through to the wiki but it went over my head. Can someone please explain it in an easier fashion? Mehul Arora · 2 years, 2 months ago

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Have you tried the Brilliant wiki on it ? Azhaghu Roopesh M · 2 years, 2 months ago

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@Azhaghu Roopesh M Yeah.. I didn't learn much. The wiki must be good though it went over my head. Mehul Arora · 2 years, 2 months ago

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@Mehul Arora 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!) Azhaghu Roopesh M · 2 years, 2 months ago

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@Azhaghu Roopesh M Can you give me some links (apart from AoPS) Mehul Arora · 2 years, 2 months ago

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@Mehul Arora Hmm ,strange . I couldn't find any good pdf for this topic . But try it out yourself and if you have any doubt in it , ask here and I'll only be glad to help you out :) Azhaghu Roopesh M · 2 years, 2 months ago

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@Mehul Arora Do you have Hall and Knight ? If so , please check pg 468 . Azhaghu Roopesh M · 2 years, 2 months ago

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@Azhaghu Roopesh M Nope.. Which class is it aimed at? Mehul Arora · 2 years, 2 months ago

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@Mehul Arora It's just a ref. book for Algebra . Azhaghu Roopesh M · 2 years, 2 months ago

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@Prasun Biswas @Calvin Lin @Rajdeep Dhingra @Azhaghu Roopesh M Please help.. :/ Mehul Arora · 2 years, 2 months ago

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@Mehul Arora 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". Prasun Biswas · 2 years, 2 months ago

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

Wah wah!! XD Mehul Arora · 2 years, 2 months ago

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