# Proof

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#2

(Original post by

Prove that is an even number.

How is this deduced? What should I be thinking about in order to derive a sequence of logical steps leading to the solution?

**Illidan2**)Prove that is an even number.

How is this deduced? What should I be thinking about in order to derive a sequence of logical steps leading to the solution?

then think what you could do with the expression...

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#3

**Illidan2**)

Prove that is an even number.

How is this deduced? What should I be thinking about in order to derive a sequence of logical steps leading to the solution?

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#5

Think about the relationship between n and n-1. When n is odd, what is n-1? When n is even, what is n-1?

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#6

(Original post by

When I factorise I get , do I not? So the parity of -1 is odd, but n can in itself be even or odd as n can be any number, right? I'm not sure where I should go from there, or if what I have done is even the logical form of progression one would make when trying to prove that .

**Illidan2**)When I factorise I get , do I not? So the parity of -1 is odd, but n can in itself be even or odd as n can be any number, right? I'm not sure where I should go from there, or if what I have done is even the logical form of progression one would make when trying to prove that .

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#7

**Illidan2**)

When I factorise I get , do I not? So the parity of -1 is odd, but n can in itself be even or odd as n can be any number, right? I'm not sure where I should go from there, or if what I have done is even the logical form of progression one would make when trying to prove that .

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#9

(Original post by

When n is odd, n-1 is even.

When n is odd, n(n-1) is even.

When n is even, n-1 is odd.

When n is even, , n(n-1) is even.

I notice that in both cases of , or , the result is even. I think I know how to prove this now. Give me a few minutes...

**Illidan2**)When n is odd, n-1 is even.

When n is odd, n(n-1) is even.

When n is even, n-1 is odd.

When n is even, , n(n-1) is even.

I notice that in both cases of , or , the result is even. I think I know how to prove this now. Give me a few minutes...

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Oh. I'm allowed to just write that as my proof? If I were to write something to that effect in an A-Level exam(naturally, I assume i'll be proving something more complex), would I receive the marks? Can I prove it in sentences? I thought I had to figure out some method of conversion into algebra that expresses my thoughts in a logical way. Am I overthinking it?

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#11

(Original post by

Oh. I'm allowed to just write that as my proof? If I were to write something to that effect in an A-Level exam(naturally, I assume i'll be proving something more complex), would I receive the marks? Can I prove it in sentences? I thought I had to figure out some method of conversion into algebra that expresses my thoughts in a logical way. Am I overthinking it?

**Illidan2**)Oh. I'm allowed to just write that as my proof? If I were to write something to that effect in an A-Level exam(naturally, I assume i'll be proving something more complex), would I receive the marks? Can I prove it in sentences? I thought I had to figure out some method of conversion into algebra that expresses my thoughts in a logical way. Am I overthinking it?

If you REALLY want to be more rigorous about it, you can say that in each case you have or then in each case you can proceed to work with algebra and factor out a 2 to show that the product is even.

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Oh, I see. Thank you so much! :3

Proof by cases(or exhaustion), is part of the specification for the A-Level Maths course I am working my way through, as well as deduction, counter-example and contradiction. Is proof by cases a derivative of proof by deduction? My textbook had that question listed as a "proof by deduction". I assume that because proof by cases is listed as part of the Edexcel A-Level Maths 2017 linear specification, it may be possible that I may encounter a question requiring me to use proof by cases?

Proof by cases(or exhaustion), is part of the specification for the A-Level Maths course I am working my way through, as well as deduction, counter-example and contradiction. Is proof by cases a derivative of proof by deduction? My textbook had that question listed as a "proof by deduction". I assume that because proof by cases is listed as part of the Edexcel A-Level Maths 2017 linear specification, it may be possible that I may encounter a question requiring me to use proof by cases?

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#13

Well an easy way to do it is notice these are consecutive numbers and therefore the product is even.

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#14

**Illidan2**)

Oh. I'm allowed to just write that as my proof? If I were to write something to that effect in an A-Level exam(naturally, I assume i'll be proving something more complex), would I receive the marks? Can I prove it in sentences? I thought I had to figure out some method of conversion into algebra that expresses my thoughts in a logical way. Am I overthinking it?

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#15

(Original post by

Oh, I see. Thank you so much! :3

Proof by cases(or exhaustion), is part of the specification for the A-Level Maths course I am working my way through, as well as deduction, counter-example and contradiction. Is proof by cases a derivative of proof by deduction? My textbook had that question listed as a "proof by deduction". I assume that because proof by cases is listed as part of the Edexcel A-Level Maths 2017 linear specification, it may be possible that I may encounter a question requiring me to use proof by cases?

**Illidan2**)Oh, I see. Thank you so much! :3

Proof by cases(or exhaustion), is part of the specification for the A-Level Maths course I am working my way through, as well as deduction, counter-example and contradiction. Is proof by cases a derivative of proof by deduction? My textbook had that question listed as a "proof by deduction". I assume that because proof by cases is listed as part of the Edexcel A-Level Maths 2017 linear specification, it may be possible that I may encounter a question requiring me to use proof by cases?

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I just checked the solution online. They deduced it by saying "If n is even, n-1 is odd and even*odd=even", and then repeated that for n being odd. Is that proof by deduction or cases?

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#17

(Original post by

I just checked the solution online. They deduced it by saying "If n is even, n-1 is odd and even*odd=even", and then repeated that for n being odd. Is that proof by deduction or cases?

**Illidan2**)I just checked the solution online. They deduced it by saying "If n is even, n-1 is odd and even*odd=even", and then repeated that for n being odd. Is that proof by deduction or cases?

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