Sum of Odd #s is the Squares 1

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  1. What does picture A have to do with picture B?
  2. Continue both A and B for two more steps.
  3. Find the totals in A. What kind of numbers are they?
  4. Does B tell you why these numbers are what they are? Explain.
  5. What is 1 + 3 + 5 + 7 + . . . + 99?


Show/Hide Solution

  1. You can find each number in the picture.
  3. 1, 4, 9, 16, 25, 36: perfect squares.
  4. You can see the squares!
  5. 1 + 3 = 4 = 22 = ((1 + 3)/2)2
    1 + 3 + 5 = 9 = 32 = ((1 + 5)/2)2
    1 + 3 + 5 + 7 = 16 = 42 = ((1 + 7)/2)2
    So 1 + 3 + 5 + … + 99 = ((1 + 99)/2)2 = 502 = 2500

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