Question

1加x的三分之一次方和的6次方乘以1加x的负的四分之一次方和的10次方展开式中的常数项是多少?

Answer 1

[1+x^(1/3)]^6 * [(1+x(^-1/4)]^10

常数项是

{C6(0)1^6[x^(1/3)]^0+C6(3)1^3[x^(1/3)]^3+C6(6)1^0[x^(1/3)]^6}{C10(0)1^10[x^(-1/4)]^0+C10(4)1^4[x^(-1/4)]^4+C10(8)1^8[x^(-1/4]^8}

=(1+20x+x^2)[1+210x^(-x)+18x^(-2)]

=1+4200+18

=4219