If n is an even integer, how can we express the odd integer that comes right after?
See solution
Practice makes perfect
Inductive reasoning uses specific examples to find patterns in order to form a conjecture. Let's try and add three odd numbers a few times and see what happens:
First trial:& 1+1+3 =5
Second trial:& 3+5+7 =15
Third trial:& 5+7+9 =21
Fourth trial:& 7+9+11=27What do all of these numbers have in common? Well, for one, they are all odd.
5/2=2.5, 15/2=7.5, 21/2=10.5, 33/2=16.5
Let's use deductive reasoning to prove this conjecture. If we let x, y, and z represent arbitrary numbers, then (2x+1) is an arbitrary odd number, as are (2y+1) and (2z+1). If we add these, we can prove that the sum of three odd integers is odd.
