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Cuestionario: Teorema del Binomio

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Cuestionario: Teorema del Binomio

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Quiz sobre el teorema del binomio

Created by

Jefferson Guancha
Jefferson Guancha
Ecuador

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Cuestionario: Teorema del Binomio
 

Cuestionario: Teorema del BinomioOnline version

Quiz sobre el teorema del binomio

by Jefferson Guancha
1

¿Cuál es la forma general de la expansión de (a+b)^n según el teorema del binomio?

2

Qué representa C(n,k) en la expansión (a+b)^n?

3

En (x+y)^5, ¿cuál es el coeficiente de x^3y^2?

4

Si n=4, ¿ cuántos términos tiene la expansión de (a+b)^n?

5

Qué caso especial del teorema del binomio se usa cuando uno de los términos es 1?

6

¿Qué teorema relaciona las potencias y coeficientes para (a+b)^n con combinaciones?

7

En la expansión de (2x+y)^3, ¿cuál es el término con x^2y?

8

Si n es 6, ¿ cuántos coeficientes diferentes aparecen en la expansión de (a+b)^n?

9

¿Cuál es el coeficiente de a^0b^6 en (a+b)^6?

10

¿Qué valor de k se usa para obtener el término a^{n} en la expansión de (a+b)^n?

Explicación

La fórmula usa coeficientes binomiales C(n,k).

C(n,k) es el coeficiente binomial que multiplica a^{n-k}b^k.

Coeficiente C(5,2)=10 para x^{5-2}y^2.

Tiene n+1 términos.

Cuando b=1, se obtiene (a+1)^n.

El teorema del binomio es el que da la expansión.

Para x^2y, k=1 en la forma (ax+by)^3.

Hay n+1 coeficientes desde C(6,0) hasta C(6,6).

Coeficiente C(6,6)=1 corresponde a a^0b^6.

El término a^{n} corresponde a k=0.

 
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