Question

o coeficiente de x15 no desenvolvimento de (x2+x-3)15

Answer 1

TK+1=(N,k).a^n-k.b^p


Tk+1=(15,k).(x^2)^15-k.(x^-3)^k


x^30-2k•x^-3k=x^15


x^30-2k-3k=x^15

igualando os expoentes:


30-2k+3k=15

-5k=15-30

-5k=-15

k=-15/-5

k=3

Tk+1=(15,k).(x^2)^15-k.(x^-3)^k


T4=(15,3).(x^2)^12.(x)^-6

T4=(15,3).(x)^24.(x)^-6


T4=(15,3).(x)^24-6

T4=(15,3).(x)^15

T4=15!//(15-3)!3!.(x)^15

T4=15!/12!3!.(x)^15

T4=15.14.13/3!

T4=7.30.13/6.(x)^15

T4=7.5.13.x^15

T4=455x^15

espero ter ajudado!


boa noite!