Chapter 8.4, Problem 9E

Find the coefficient of x¹⁰in the power series of each of these functions.

a) ${\left(1+x^5+x^{10}+x^{15}+\mathrm{...}\right)}^3$

b) ${\left(x^3+x^4+x^5+x^6+x^7+\mathrm{...}\right)}^3$

c) $\left(x^4+x^5+x^6\right)\left(x^3+x^4+x^5+x^6+x^7\right)\left(1+x+x^2+x^3+x^4+\mathrm{...}\right)$

d) $\left(x^2+x^4+x^6+x^8+\mathrm{...}\right)\left(x^3+x^6+x^9+\mathrm{...}\right)\left(x^4+x^8+x^{12}+\mathrm{...}\right)$e) $\left(1+x^2+x^4+x^6+x^8+\mathrm{...}\right)\left(1+x^4+x^8+x^{12}+\mathrm{...}\right)\left(1+x^6+x^{12}+x^{18}+\mathrm{...}\right)$