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Cuestionario: Binomio de Newton

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Cuestionario: Binomio de Newton

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Repaso rápido del binomio de Newton

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luis rojas
luis rojas
Ecuador

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Cuestionario: Binomio de Newton
 

Cuestionario: Binomio de NewtonOnline version

Repaso rápido del binomio de Newton

by luis rojas
1

¿Qué dice el teorema binomial de Newton para (a+b)^n?

2

¿Qué representa C(n,k) en la expansión?

3

En la expansión de (a+b)^4, ¿cuál es el término con a^2 b^2?

4

¿Cuántos términos tiene la expansión de (a+b)^n?

5

¿Qué nombre recibe la lista de coeficientes en la expansión de (a+b)^n?

6

Si n=3, ¿cuál es el coeficiente de a^2 b en la expansión de (a+b)^3?

7

¿Qué propiedad tiene los coeficientes C(n,k) respecto a k y n?

8

¿Cómo se llama la forma general del término k en la expansión?

9

Si se toma a=1, ¿qué representa la expansión de (1+b)^n?

10

Qué indica el término n en la expansión?

Explicación

Es la expansión por coeficientes binomiales C(n,k).

C(n,k) son los coeficientes de la expansión, formados por n choose k.

El coeficiente para a^2 b^2 es C(4,2)=6.

La expansión contiene n+1 términos, correspondientes a k=0..n.

Los coeficientes forman las filas del Triángulo de Pascal.

Coeficiente C(3,1)=3 para a^{2}b.

Propiedad de simetría: coeficientes son iguales para k y n-k.

Término general: C(n,k) a^{n-k} b^k.

Al sustituir a=1, cada término es C(n,k) b^k y suman.

n es el exponente y determina la cantidad de términos.

 
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