Sender: JOHN
Subject: Help the Helper!
Date: Sun, 20 Sep 1998 10:50:28 -0400
I am TRYING to help my niece with her Community College Teacher's math course! I have a BS and an Engineer yet stumble on what her book is asking:
- Fill in the blanks to continue this sequence of equations:
| 1 | = | 0+1 |
| 1+3+1 | = | 1+4 |
| 1+3+5+3+1 | = | 4+9 |
| _______________ | = | ____ |
| _______________ | = | ____ |
- What expression, suggested by part (1.), should be placed in the blank to complete this equation?
| 1 + 3 + 5.........+ (2n-3) + (2n-1)+ (2n-3)+...+5 + 3+ 1 | = | _________ |
hint: The number preceding n is n - 1.
I am lost as to just what they are trying to do? Is it related to Pascal's Triangle and are they merely playing games with the student to expose them to numerology???
John, Thanks
Hi John,
I think they are trying to have the students see a pattern.
If you complete two more rows you get
| 1 | = | 0+1 |
| 1+3+1 | = | 1+4 |
| 1+3+5+3+1 | = | 4+9 |
| 1+3+5+7+5+3+1 | = | 9+16 |
| 1+3+5+7+9+7+5+3+1 | = | 16+25 |
This suggests that the general expression in part 2. should be the sum of two squares.
Now look at the last equation
1+3+5+7+9+7+5+3+1 = 16+25 (= 4^2 + 5^2).
This is a particular instance of the general expression in 2. with the middle term on the left equal to 9, that is 2n-1 = 9 so n = 5. You should now be able to guess the expression to place in the blank for part 2.
Cheers
Penny
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