Need Help

Can someone Explain Newton's Sums to me?

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

Thanks in advance.

#Algebra

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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

Rajdeep Dhingra - 6 years, 2 months ago

When's your vacation going to be over ?

A Former Brilliant Member - 6 years, 2 months ago

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

Rajdeep Dhingra - 6 years, 2 months ago

@Rajdeep Dhingra – Ok. Enjoy :)

A Former Brilliant Member - 6 years, 2 months ago

Do you still need help ?

Rajdeep Dhingra - 6 years, 2 months ago

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

Mehul Arora - 6 years, 2 months ago

Start solving questions :)

A Former Brilliant Member - 6 years, 2 months ago

@A Former Brilliant Member – Yeah.. I am trying. Just learnt Vieta's. Trying to perfect it. :)

Mehul Arora - 6 years, 2 months ago

@Mehul Arora – Best of luck :)

A Former Brilliant Member - 6 years, 2 months ago

@A Former Brilliant Member – Thanks!!

Mehul Arora - 6 years, 2 months ago

Ok. Where do you have a doubt ?

Rajdeep Dhingra - 6 years, 2 months ago

@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 - 6 years, 2 months ago

@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 - 6 years, 2 months ago

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

Mehul Arora - 6 years, 2 months ago

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 - 6 years, 2 months ago

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

Wah wah!! XD

Mehul Arora - 6 years, 2 months ago

Have you tried the Brilliant wiki on it ?

A Former Brilliant Member - 6 years, 2 months ago

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

Mehul Arora - 6 years, 2 months ago

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!)

A Former Brilliant Member - 6 years, 2 months ago

@A Former Brilliant Member – Can you give me some links (apart from AoPS)

Mehul Arora - 6 years, 2 months ago

@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 :)

A Former Brilliant Member - 6 years, 2 months ago

@Mehul Arora – Do you have Hall and Knight ? If so , please check pg 468 .

A Former Brilliant Member - 6 years, 2 months ago

@A Former Brilliant Member – Nope.. Which class is it aimed at?

Mehul Arora - 6 years, 2 months ago

@Mehul Arora – It's just a ref. book for Algebra .

A Former Brilliant Member - 6 years, 2 months ago

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 - 6 years, 2 months ago

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 - 6 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$