A soma dos coeficientes do desenvolvimento de (2x + y)m é 729....
A soma dos coeficientes do desenvolvimento de (2x + y)m é 729. Nesse caso, Am = 3.Bm = 4.Cm = 5.Dm = 6.Em = 10. #QuestõesdeConcurso
1 Resposta
Ver resposta
![(2x+y)^5]()
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^{1}b^{n-1}+dbinom{n}{n}a^0b^{n}]()
Assim:
![(2x+y)^5=dbinom{5}{0}(2x)^5y^0+dbinom{5}{1}(2x)^4y^1+dots+dbinom{5}{4}(2x)^1y^4+dbinom{5}{5}(2x)^0y^5]()
A soma dos coeficientes de
é:
![dbinom{5}{0}2^5+dbinom{5}{1}2^4+dbinom{5}{2}2^3+dbinom{5}{3}2^2+dbinom{5}{4}2^1+dbinom{5}{5}2^0]()
![=2^5+5cdot2^4+10cdot2^3+10cdot2^2+5cdot2+1]()
![=32+80+80+40+10+1=243]()
Alternativa C
![(2x+y)^5](/image/0587/5751/c18d8.png)
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^{1}b^{n-1}+dbinom{n}{n}a^0b^{n}](/image/0587/5751/d9757.png)
Assim:
![(2x+y)^5=dbinom{5}{0}(2x)^5y^0+dbinom{5}{1}(2x)^4y^1+dots+dbinom{5}{4}(2x)^1y^4+dbinom{5}{5}(2x)^0y^5](/image/0587/5751/a4491.png)
A soma dos coeficientes de
![(2x+y)^5](/image/0587/5751/c18d8.png)
![dbinom{5}{0}2^5+dbinom{5}{1}2^4+dbinom{5}{2}2^3+dbinom{5}{3}2^2+dbinom{5}{4}2^1+dbinom{5}{5}2^0](/image/0587/5751/d352e.png)
![=2^5+5cdot2^4+10cdot2^3+10cdot2^2+5cdot2+1](/image/0587/5751/bcbd8.png)
![=32+80+80+40+10+1=243](/image/0587/5751/417a1.png)
Alternativa C
Sua resposta
Mais perguntas de Matemática
![Toda Materia](https://escolaeducacao.org/assets/images/element/01.webp)
Você tem alguma dúvida?
Faça sua pergunta e receba a resposta de outros estudantes.