An interesting mathematical property

[jaquecusto]

3^3 = [3^3 - 3^2] +[3^2 - 3^1] + [3^1 - 3^0] + 3^0

Practical Demonstration:

27 = [27-9] + [9-3] + [3-1] + 1

27 = 18 +6+2+1

27 = 27

Is this property discussed in theory of games?

 

[pmsrw3]

I don't understand. What does this have to do with game theory?

 

[gb7nash]

I'm not sure how this has anything to do with game theory, but what you just found is what's called the collapsing sum.

 

[pmsrw3]

I'm not sure how this has anything to do with game theory, but what you just found is what's called the collapsing sum.

What is that, exactly? I'm unclear on what the "interesting property" is. Obviously you can express any number as a sum of differences between a series of smaller numbers. I tried googling "collapsing sum" but found nothing helpful.

 

[micromass]

What is that, exactly? I'm unclear on what the "interesting property" is. Obviously you can express any number as a sum of differences between a series of smaller numbers. I tried googling "collapsing sum" but found nothing helpful.

I think he means a telescoping series: http://en.wikipedia.org/wiki/Telescoping_series of which the OP gave a (trivial) example.

 

[gb7nash]

I think he means a telescoping series: http://en.wikipedia.org/wiki/Telescoping_series of which the OP gave a (trivial) example.

Yes. Thank you.