Question 1044051: prove, using the direct method of proof, that if n is a natural number, n(n+1) is an even number.
Found 2 solutions by josgarithmetic, robertb:
Answer by josgarithmetic(39630)   (Show Source):
You can put this solution on YOUR website! Not sure about the method of proving, but
n=1, 1(1+1)=1*2, EVEN;
n=2, 2(2+1), EVEN;
n=3, 3(3+1)=3*4, EVEN;
and continue...
Each of the two factors alternates in even and odd, so the product will stay even.
Answer by robertb(5830)  (Show Source):
You can put this solution on YOUR website! For any two consecutive integers n and n+1, one of them is always divisible by 2, or, is even, and the other one, odd.
===> Their product n(n+1) is always even.
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