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 *n*th even number is 2*n*.

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

(a) Explain why.

(b) Write down an expression, in terms of *n*, for the next even number after 2*n* + 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 (3*n* + 1)^{2} – (3*n* –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

DillyEdited by

Dilly on Sat 9th June, 2012 @ 21:09