Question

The sum of any two consecutive odd numbers is always odd. True or false?

Answer 1

I know its false but how can i prove it

Answer 2

False

Answer 3

1+3 =
3+5 =
5+7=


try these and u get it

Answer 4

3+5=8

Answer 5

i did a few of those and saw its false . Can i prove by contradicting myself?

Answer 6

Let k be any integer

2k is always even

2k+1 is always odd

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let the first integer be 2k+1

the next integer up is (2k+1) + 2 = 2k+3

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so the two consecutive even integers is 2k+1 and 2k+3

Answer 7

add them up: (2k+1)+(2k+3) = 4k + 4 = 2*(k+1)

we have something in the form 2*m, where m is an integer and m = k+1

so the sum is always even

Answer 8

this is also true for any two odd numbers as well (proof is a bit different though, but follows the same basic idea)

Answer 9

Thank you so much @jim_thompson5910

Answer 10

ya so if 5+7= 12
then its false for every other problem

Answer 11

What about if the sum of any three consecutive integers is always divisible by 3.
1+2+3= 6
2+3+4= 9
3+4+5= 12
4+5+6= 15

all these results are divisible by 3.

Answer 12

@jim_thompson5910 ^

Answer 13

let x be the first integer

x+1 is the next integer after that

(x+1)+1 = x+2 is the next one after that

Answer 14

add them up:

(x) + (x+1) + (x+2)

x + x+1 + x+2

3x + 3

3*(x+1)

so that claim is true because 3 is a factor of 3*(x+1)

Answer 15

Oh i see it now! That makes more sense!