Problem:
Learning to recognize patterns which suggest general truths.
For example looking at the statements.
3+5=8, 9+5=14, 11+17=28
you might guess that the sum of two odd numbers is an even number. Can you think of two odd numbers whose sum is an odd number?

Consider these statements:
If 3+5=9, 5+7+11=23, 9+13+21=43
a.) Complete this generalization
If a,b and c are three odd numbers, then a+b+c is ____________
b.) Can you establish the truth of this generalization?

Please help and show your solution please... :D

1

Answers

2015-06-06T20:57:52+08:00

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
For the problem above, no I cannot think of two numbers whose sum is an odd number.

Consider these statements:
If 3+5=8   5+7+11 = 23    9+13+21=43
a) If a,b,c are three odd numbers then a+b+c is an odd number as well.

b) An odd number is represented by 2m+1 with m∈Z

So we let:
a = 2x+1
b = 2y+1
c = 2z + 1

with x,y,z∈Z

To show that the statement above about the sum of two number being even:
a + b = (2x+1) + (2y+1) = 2x+2y+2 = 2(x+y+1)
Therefore it is TRUE

but is it true that 3 odd numbers have a sum that is odd?
a + b + c = (2x+1) + (2y+1) + (2z+1) = 2x + 2y + 2z + 3= = 2(x+y+z+1) + 1
We let x+y+z+1=m, since x,y,z are integers then m is an integer as well:
a+b+c = 2m + 1
This has the same form as above
Therefore the sum of three odd numbers is odd
0