# maths proofs

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are these correct?

1.)

Prove that 2 consecutives numbers multiplied are even...

(2n) (2n+1) = 4n^2 + 2n

and since 2n + 2n proves that 2 evens added must be even and both the number in the above answer are even (both divide by 2) so will be even.

2.)

Prove that any 3 consecutive numbers are divisible by 3?

(x)(x+1)(x+2) = 3(x+1)

if the second one is correct then how do you get 3(x+1) from factorising the brackets?

1.)

Prove that 2 consecutives numbers multiplied are even...

(2n) (2n+1) = 4n^2 + 2n

and since 2n + 2n proves that 2 evens added must be even and both the number in the above answer are even (both divide by 2) so will be even.

2.)

Prove that any 3 consecutive numbers are divisible by 3?

(x)(x+1)(x+2) = 3(x+1)

if the second one is correct then how do you get 3(x+1) from factorising the brackets?

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#2

(Original post by

are these correct?

1.)

Prove that 2 consecutives numbers multiplied are even...

(2n) (2n+1) = 4n^2 + 2n

and since 2n + 2n proves that 2 evens added must be even and both the number in the above answer are even (both divide by 2) so will be even.

2.)

Prove that any 3 consecutive numbers are divisible by 3?

(x)(x+1)(x+2) = 3(x+1)

if the second one is correct then how do you get 3(x+1) from factorising the brackets?

**blag dahlia112**)are these correct?

1.)

Prove that 2 consecutives numbers multiplied are even...

(2n) (2n+1) = 4n^2 + 2n

and since 2n + 2n proves that 2 evens added must be even and both the number in the above answer are even (both divide by 2) so will be even.

2.)

Prove that any 3 consecutive numbers are divisible by 3?

(x)(x+1)(x+2) = 3(x+1)

if the second one is correct then how do you get 3(x+1) from factorising the brackets?

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#3

(Original post by

are these correct?

2.)

Prove that any 3 consecutive numbers are divisible by 3?

(x)(x+1)(x+2) = 3(x+1)

if the second one is correct then how do you get 3(x+1) from factorising the brackets?

**blag dahlia112**)are these correct?

2.)

Prove that any 3 consecutive numbers are divisible by 3?

(x)(x+1)(x+2) = 3(x+1)

if the second one is correct then how do you get 3(x+1) from factorising the brackets?

(x) + (x+1) + (x+2) = 3x + 3

= 3 (x+1)

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#4

In the second,

x(x+1)(x+2) = x(x^2+3x+3) = x^3+3x^2+3x and the multiplications by 3 ensure a result divisible by 3... I think...

x(x+1)(x+2) = x(x^2+3x+3) = x^3+3x^2+3x and the multiplications by 3 ensure a result divisible by 3... I think...

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what Expression sed is right so (hopefully) i just copied out the qu. wrong

ZJuwellH is wrong because of the addition which could make it wrong i think? because it would divide by 3 but then x^3 is added so i'm not sure if it would still divide by 3

ZJuwellH is wrong because of the addition which could make it wrong i think? because it would divide by 3 but then x^3 is added so i'm not sure if it would still divide by 3

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#6

**blag dahlia112**)

are these correct?

1.)

Prove that 2 consecutives numbers multiplied are even...

(2n) (2n+1) = 4n^2 + 2n

and since 2n + 2n proves that 2 evens added must be even and both the number in the above answer are even (both divide by 2) so will be even.

2.)

Prove that any 3 consecutive numbers are divisible by 3?

(x)(x+1)(x+2) = 3(x+1)

if the second one is correct then how do you get 3(x+1) from factorising the brackets?

If the second is the product of three consecutive numbers, then one of the three must be a multiple of three. Therefore, it will have 3 as a factor.

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#7

(Original post by

what Expression sed is right so (hopefully) i just copied out the qu. wrong

ZJuwellH is wrong because of the addition which could make it wrong i think? because it would divide by 3 but then x^3 is added so i'm not sure if it would still divide by 3

**blag dahlia112**)what Expression sed is right so (hopefully) i just copied out the qu. wrong

ZJuwellH is wrong because of the addition which could make it wrong i think? because it would divide by 3 but then x^3 is added so i'm not sure if it would still divide by 3

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yeah ok i think i've got it all now

thanks

btw do you know any other possible proofs involving consecutive numbers which have appeared on past gcse papers?

thanks

btw do you know any other possible proofs involving consecutive numbers which have appeared on past gcse papers?

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#9

(Original post by

Nice way to write your solution to the first one would simply be to take out the two giving 2(2n^2+n). Since this is divisible by two, it mus be even.

If the second is the product of three consecutive numbers, then one of the three must be a multiple of three. Therefore, it will have 3 as a factor.

**meepmeep**)Nice way to write your solution to the first one would simply be to take out the two giving 2(2n^2+n). Since this is divisible by two, it mus be even.

If the second is the product of three consecutive numbers, then one of the three must be a multiple of three. Therefore, it will have 3 as a factor.

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yeah i think expression got it right though and i probably wrote down the question one

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#11

you could say that in any two consecutive numbers, one is even and one is odd, and an even times an odd is always even.

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