Respostas

2014-09-03T15:10:10-03:00
 \frac{1.x^{6}k^{0}}{0}  +  \frac{x^{5}k^{1}}{1} +   \frac{x^{4}k^{2}}{2} +  \frac{x^{3}k^{3}}{3} +  \frac{x^{2}k^{4}}{4} +  \frac{x^{1}k^{5}}{5} + \frac{x^{0}k^{6}}{6}
Multiplicando o 1 na frente do x vezes o expoente do x fica dividindo pelo denominador do proximo;
x^6} + 6x^5.k^1 + 15x^4.k^2 + 20^3.k^3 + 15x^2.k^4 + 6x^1.k^5 + k^6


A melhor resposta!
  • Usuário do Brainly
2014-09-03T15:14:28-03:00
A n-ésima linha do triângulo de pascal é:

\dbinom{n}{0}~\dbinom{n}{1}~\dots~\dbinom{n}{n-1}~\dbinom{n}{n}

A sexta linha é:

\dbinom{6}{0}~\dbinom{6}{1}~\dbinom{6}{2}~\dbinom{6}{3}~\dbinom{6}{4}~\dbinom{6}{5}~\dbinom{6}{6}

Em geral,

(a+b)^{n}=\dbinom{n}{0}a^{n}b^{0}+\dbinom{n}{1}a^{n-1}b^1+\dots+\dbinom{n}{n-1}a^1b^{n-1}+\dbinom{n}{n}a^{0}b^{n}.
Com isso,

(x+k)^6=

\dbinom{6}{0}x^6k^0+\dbinom{6}{1}x^5k^1+\dbinom{6}{2}x^4k^2+\dbinom{6}{3}x^3k^3+\dbinom{6}{4}x^2k^4+\dbinom{6}{5}x^1k^5+\dbinom{6}{6}x^0k^6

(x+k)^6=x^6+6x^5k+15x^4k^2+20x^3k^3+15x^2k^4+6xk^5+k^6






3 5 3