User talk:Devoutb3nji

Edits to Binomial coefficient

Welcome to Wikipedia. I see you have edited Binomial coefficient, adding the following material

The Binomial Theorem also is apparent in a ρ^th sum of a series (usually beginning with (1)).

$\sum _{\alpha =1}^{x}1$ (1)

When continued on until the set limit (ρ) the summation expression alters with a set range of factorial relationships: specifically, the factorial of the stated variable by which summation is measured (in the above case: x) added to the limit (ρ) with one subtracted (as to allow for the fact that the first summation must include the original series with no α value in the component) divided by $(x-1)!$ as to permit the value from x to be produced from the first series relationship (2).

$\sum _{\alpha =1}^{x}1={x}$ (2)

Thus we can gain the expression for a ρ^th summation which as is clearly visible yields the division of two factorials implicating the usage of the Binomial Expansion (3) for this ρ^th degree summation polynomial deriving from the base form (1), note that the symmetry of the Binomial Coefficient indicates that the coefficient of ρ and x-1 will be identical:

${\frac {(x+\rho -1)!}{(x-1)!\rho !}}={x+\rho -1 \choose \rho }$ (3)

Substituting ρ=1 yields (4):

${\frac {x!}{(x-1)!}}=x=\sum _{\alpha =1}^{x}1$ (4)

I presume you added this in good faith, but it is unclear what this is about (for instance what ρ is or which series is meant), or why it should be in the section where it appears. In fact I cannot make any sense out of it, nor I suppose can the average reader; I will therefore remove it. If you wish to add this to the article, please make your intentions more clear. Marc van Leeuwen (talk) 15:28, 7 April 2010 (UTC)

Ok, thank you for amending the expression graphics anyhow - I may clarify this with an extension paragraph at some point.