In this section, we see how can be used to derive another useful identity. We begin by establishing a different recursive formula for P(p,k) than was used in our definition of it.
An Application of the Binomial Theorem
In this section, we see how can be used to derive another useful identity. We begin by establishing a different recursive formula for \(P(p,k)\) than was used in our definition of it.
Our goal in this section will be to invoke with the exponent \(p=-1/2\). To do so in a meaningful manner, we need a simplified expression for \(C(-1/2,k)\), which the next lemma provides.
We will return to this generating function in , where it will play a role in a seemingly new counting problem that actually is a problem we've already studied in disguise.
Now recalling about the coefficients in the product of two generating functions, we are able to deduce the following corollary of by squaring the function \(f(x) = (1-4x)^{-1/2}\).
Sasa
Hakuna kifaa cha kupigia hesabu kinachoweza kufanya hesabu, lakini kifaa hicho kinaweza kutumiwa katika hesabu.
Keep your own working
Akaunti la bure laongezea mambo makuu juu ya kila somo, rekodi ya yale ambayo umemaliza, matatizo yako ya kutatua katika sehemu moja, na mtunzaji unayeweza kuuliza juu ya ukurasa huu.
Vaa alama yoyote ya ufafanuzi kamili, picha, na maana ya kila herufi.
Maana ya kila sehemu
Wazia hilo
Inastahili Kujua
Vielelezo
Pia, ufafanuzi huo ulitumiwa
Maswali ambayo watu huuliza
Permutation or combination?
Ask whether order matters. A lock code is a permutation (order matters); a hand of cards is a combination (it does not).
What is a graph in this sense?
Dots (vertices) joined by lines (edges), not a plot. Road maps, social networks and molecules are graphs; questions like "is there a route" and "how few colours" are graph theory.
Sehemu za ukurasa huu zimebadilishwa kutoka kwa
Keller & Trotter, Applied Combinatorics (CC BY-SA 4.0).
Tumekamatwa na kukosolewa tena hapa; makosa ni yetu.