SOLUTION: `Take a look at the following sums: 1=1 1+3=4 1+3+5=9 1+3+5+7=16 1+3+5+7+9=25 a. Come up with a conjecture about the sum when you add the first n odd numbers. For examp

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Question 1046510: `Take a look at the following sums:
1=1
1+3=4
1+3+5=9
1+3+5+7=16
1+3+5+7+9=25
a. Come up with a conjecture about the sum when you add the first n odd numbers. For example when you added the first five odd numbers ( 1+3+5+7+9) what do you get? What if I wanted to add the first 10 odd numbers? Or 100?
b. Can you think of a geometric interpretation of this pattern? If you start with one square and add on three more, what can you make? If you now have four squares and you add on five more, what can you make?
c. Is there a similar pattern for adding the first n even numbers?
2=2
2+4=6
2+4+6=12
2+4+6+8= 20
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


The sum of the first odd numbers is .

Induction Proof:

Prove:


Initial Step:




Induction Step:
Show:


Assume:



Then



so



Substitute from the assumption:



But



Therefore, if the assertion is true for some , then it is true for . QED.

John

My calculator said it, I believe it, that settles it
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