Proofs........i just don't get them!

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ANY HELP WITH UNDERTSANDING PROOFS,WOULD BE MARVELLOUS!I JUST DON'T SEEM T UNDERTSAND THEM,--EDEXCEL LINEAR A---

HERE'S AN EXAMPLE:Prove using algebra ,that the sum of two consecutive numbers is always odd number?(3m)

PLEASE HELP ME!:)

Posted Sat 9th June, 2012 @ 18:33 by anonymous

9 Answers

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For algebraic proofs you always use letters i.e. for even numbers I usually use 2n (even numbers are always a multiple of two) and therefore odd numbers are 2n+1 (odd numbers are one more (or one less) than even numbers) and consecutive numbers are n-1,n, n+1, n+2 where n is an integer( a whole number)

So here I would write, 

Let the two consecutive numbers be n and n+1

so (n+1) + n = 2n+1 as the result is one more than a multiple of 2 (even) the number is odd.

I don't know how they got 3m though!

If there any other proofs you do not know about, give me an example and I can try and solve and explain it.

Hope this helps! :D

Answered Sat 9th June, 2012 @ 18:43 by Dilly
Edited by Dilly on Sat 9th June, 2012 @ 18:44
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the 3M STANDS FOR ----3 MARKS ,SORRY:l

Answered Sat 9th June, 2012 @ 18:45 by anonymous
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WHY ARE ODD NUMBERS always 2n+1?

Answered Sat 9th June, 2012 @ 18:46 by anonymous
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Oh ok thats just me being a bit dim!!

Answered Sat 9th June, 2012 @ 18:46 by Dilly
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no i think you are PRETTY smart since you knew this,btw where did you learn about the odd numbers thing?>is it in the textbook(edexcel),do i need to know any other info that is similar to this?please let me know if so:)

Answered Sat 9th June, 2012 @ 20:33 by anonymous
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2n +1 is always odd because the result is one more than a multiple of two(even). For example if n was 2, 2*2+1=5 or if n was 15, 2*15+1=31. I hope this explains it better. 

I learnt about proofs from my teacher because the textbook did not explain it well and I think thats all the things you need to know about algebraic proofs (except 3n would mean the result is a multiple of 3 or 4n would be even because it is a multiple of 4). I didn't get proofs either because I'm one of those people who think maths should only be about numbers :D, but after I practiced I got it. You just try and make the sentence into an equation by using what I said before.

You can try these and then get back to me, if you want!

 Q4.          Tarish says,

‘The sum of two prime numbers is always an even number’.

He is wrong.

Explain why. 

Q5.          The nth even number is 2n.

The next even number after 2n is 2n + 2

(a)     Explain why.

 (b)     Write down an expression, in terms of n, for the next even number after 2n + 2

(c)     Show algebraically that the sum of any 3 consecutive even numbers is always a multiple of 6

 (Total 5 marks)

Q6. Prove that (3n + 1)2 – (3n –1)2 is a multiple of 4, for all positive integer values of n.

(Total 3 marks)

The other proofs I can think of is you might get a shape with lengths in terms of x and then prove why the area or the perimeter is such a number or equation.

For example, the question on the pentagon in this document.

http://getrevising.co.uk/resources/surds_vectors_and_proof_questions

The other two proofs are congruent triangles which you can look at in this link

http://getrevising.co.uk/resources/congruent_and_similar_shapes_maths_part_3_congruent_shapes

and circle theorem proofs (which are very rare!!)

http://www.benjamin-mills.com/maths/Year11/circle-theorems-proof.pdf]

Hope this helps! If you have any more questions, just ask!


Answered Sat 9th June, 2012 @ 21:08 by Dilly
Edited by Dilly on Sat 9th June, 2012 @ 21:09
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DILLY YOU ARE MY FAVOURITE PERSON IN THE WORLD RIGHT NOW!:')

Answered Sat 9th June, 2012 @ 21:13 by anonymous
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are there any answers to these?:)

Answered Sat 9th June, 2012 @ 21:14 by anonymous
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Well you have to email the guy!! But if you don't want to tell me what answers you got, I can help!

Answered Sat 9th June, 2012 @ 21:23 by Dilly
Edited by Dilly on Sat 9th June, 2012 @ 21:23