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

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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?
 

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  • #2
Samy_A
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##(x+1)²-x²=2x+1##

This shows why the difference is always 2.
 
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  • #3
PeroK
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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?
If you spotted that you should look for a pattern in the sequence ##x^3: 1, 8, 27, 64 \dots##
 

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