SOLUTION: Show that the sum of two consecutive numbers is not even.
Algebra.Com
Question 984747: Show that the sum of two consecutive numbers is not even.
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Let x be any integer.
x and x+1 are consecutive integers, .
Either must be odd and the other must be even.
x+(x+1) is either ODD + EVEN or it is EVEN + ODD;
ODD+EVEN is ODD; and EVEN+ODD is ODD.
Neither arrangement is even.
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Maybe a better way.
, the sum of the consecutive numbers;
The summand is EVEN. It is multiple of 2 and an integer, the factor 2 ensuring 2x be even. , ODD; NOT an element of the Integers. EVEN and ODD numbers are always Integers.
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