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X^2 relation to 2x, 2x+1

  1. Dec 4, 2015 #1
    Is there a relation between the fact that the derivative of x^2 is 2x and that the difference between 1,4,9,16, ... is 3, 5, 7, 9, ...?

    And why is the difference always 2?
     
  2. jcsd
  3. Dec 4, 2015 #2

    Samy_A

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    ##(x+1)²-x²=2x+1##

    This shows why the difference is always 2.
     
  4. Dec 4, 2015 #3

    PeroK

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    If you spotted that you should look for a pattern in the sequence ##x^3: 1, 8, 27, 64 \dots##
     
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