Tentukan koefisien x^10 dalam eksprsi (x^3 + x^4 + ....)^3 kali (x+x^2 + .... + x^5)(1-x^5)^3 tolonggggggggggggggggg

[tex](x^3+x^4+x^5+...)^3\times\frac{x+x^2+...+x^5}{(1-x^5)^3}=(x^3\times (1+x+x^2+...))^3\times\frac{x(1+x+...+x^4)}{(1-x^5)^3}\\=x^9\times \frac{1}{(1-x)^3}\times x\times \frac{1-x^5}{1-x}\times \frac{1}{(1-x^5)^3}\\=x^{10}\times \frac{1}{(1-x)^4\times (1-x^5)^2}[/tex]

karena diminta koefisien x^10, berarti kita akan mencari koefisien x^0 dari
[tex]f(x)=\frac{1}{(1-x)^4\times (1-x^5)^2}[/tex]
[tex]ko.\ \ x^0\ \ dari\ \ f(x)=ko.\ \ x^0\ \ dari\ \ \frac{1}{(1-x)^4} \times ko.\ \ x^0\ \ dari\ \ \frac{1}{(1-x^5)^2}\\=1\times 1\\=1[/tex]

Materi Fungsi Pembangkit//Ekspansi