Update Math4202_L23.md

content/Math4202/Math4202_L23.md

@@ -62,7 +62,6 @@ Therefore $f$ must have a root in $B^2$.
 If $\|a_{n-1}\|+\|a_{n-2}\|+\cdots+\|a_0\|< R$ has a root in the disk $B^2_R$. (and $R\geq 1$, otherwise follows part 1)
 
 Consider $\tilde{f}(x)=f(Rx)$.
-
 $$
 \begin{aligned}
 \tilde{f}(x)
@@ -73,7 +72,7 @@ $$
 
 $$
 \begin{aligned}
-\|\frac{a_{n-1}}{R}\|+\|\frac{a_{n-2}}{R^2}\|+\cdots+\|\frac{a_0}{R^n}\|&=\frac{1}{R}\|a_{n-1}\|+\frac{1}{R^2}\|a_{n-2}\|+\cdots+\frac{1}{R^n}\|a_0\|\\
+\left\|\frac{a_{n-1}}{R}\right\|+\left\|\frac{a_{n-2}}{R^2}\right\|+\cdots+\left\|\frac{a_0}{R^n}\right\|&=\frac{1}{R}\|a_{n-1}\|+\frac{1}{R^2}\|a_{n-2}\|+\cdots+\frac{1}{R^n}\|a_0\|\\
 &<\frac{1}{R}\left(\|a_{n-1}\|+\|a_{n-2}\|+\cdots+\|a_0\|\right)\\
 &<\frac{1}{R}<1
 \end{aligned}