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

Algebra ->  Equations -> 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      Log On


   

Question 1046328: 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 ikleyn(52776) About Me  (Show Source):