Video: Dab tsi yog qhov sib npaug ntawm cov coefficients hauv ib kab ntawm Pascal daim duab peb sab?
2024 Tus sau: Edward Hancock | [email protected]. Kawg hloov kho: 2023-12-16 01:32
Theorem. Cov sum ntawm tag nrho cov nkag hauv nth kab ntawm Pascal daim duab peb sab yog 2n.
Ib yam li ib tug yuav nug, koj tuaj yeem pom cov coefficients ntawm ib kab ntawm Pascal daim duab peb sab?
Kev txiav txim siab coefficients nrog Pascal daim duab peb sab . Txhua kab muab cov coefficients rau (a + b) , pib nrog n = 0. Mus nrhiav tus binomial coefficients rau (a + b) , siv nth kab thiab ib txwm pib nrog qhov pib. Piv txwv li, binomial coefficients rau (a + b)5 yog 1, 5, 10, 10, 5, thiab 1 - nyob rau hauv qhov kev txiav txim.
Tsis tas li ntawd, tus qauv rau Pascal daim duab peb sab yog dab tsi? A Formula rau txhua qhov nkag hauv The Daim duab peb sab Lus Cim: "n xaiv k" tuaj yeem sau tau C(n, k), Ck los yog txawm Ck. Qhov "!" yog "factorial" thiab txhais tau tias yuav muab ntau tus lej ntawm cov lej qis. npr: 4! Luas = 4 × 3 × 2 × 1 = 24.
Raws li, kab nth nyob rau hauv Pascal daim duab peb sab yog dab tsi?
The n th kab ntawm Pascal daim duab peb sab yog: (n−10) (n−11) (n−12) (n−1n−1) That is: (n−1)!
Pascal formula yog dab tsi?
Hauv lej, Pascal tus txoj cai (los yog Pascal's formula ) yog ib tug combinatorial tus kheej hais txog binomial coefficients. Nws hais tias rau tus lej zoo n thiab k, qhov twg. yog binomial coefficient; ib qho kev txhais ntawm uas yog tus coefficient ntawm xk lub sij hawm nyob rau hauv expansion ntawm (1 + x).
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