Pascal Triangle: The Negative Side

[krateesh]

Can we use pascal triangle by moving upwards i.e in opposite direction,considering that the opposite side will have their pole as -1?
Mens both 1 & -1 will lie in between the centre.
And what if we remain unipolar with centre as 1?
Surely if both of them fail to give us the required results than we can say that pascal triangle is not universal as it doesn't fair well in negative world.

 

[Gib Z]

Basically you wish to extend Pascals Triangle to correspond to the coefficients of negative exponents? i.e $$(a+b)^[-n]$$. But if you recognize, this can also be expressed as $$((a+b)^n)^[-1]$$, or the reciprocal of the absolute value of your negative n. So we can still use the triangle.

Edit: Uhh this tex I am trying to use isn't going too smoothly..the weird stuff ups are ment to be exponents...

 

[CRGreathouse]

Use braces for LaTeX:
$$(a+b)^{-n}$$
$$((a+b)^n)^{-1}$$

 

[Gib Z]

o ok thanks that's what i meant