Suppose that (a(mathrm{~L})=(1-phi mathrm{L})), with (left|phi_{1} ight| <1), and (b(mathrm{~L})=1+phi mathrm{L}+phi^{2} mathrm{~L}^{2}+) (phi^{3} mathrm{~L}^{3} cdots) a. Show

Suppose that \(a(\mathrm{~L})=(1-\phi \mathrm{L})\), with \(\left|\phi_{1}\right|<1\), and \(b(\mathrm{~L})=1+\phi \mathrm{L}+\phi^{2} \mathrm{~L}^{2}+\) \(\phi^{3} \mathrm{~L}^{3} \cdots\)

a. Show that the product \(b(\mathrm{~L}) a(\mathrm{~L})=1\), so that \(b(\mathrm{~L})=a(\mathrm{~L})^{-1}\).

b. Why is the restriction \(\left|\phi_{1}\right|<1\) important?