Question 19
For each natural number $n$ It is considered the polynomial
$$
P_{n}(x)=x^{n+2}-2x+1
$$
a) Prove that the equation $P_{n}(x)=0$ It has a root $c_{n}$ and only one in the interval $(0,1)$.
b) Calculate
$$
\lim_{n \rightarrow \infty} c_{n}
$$
$$
P_{n}(x)=x^{n+2}-2x+1
$$
a) Prove that the equation $P_{n}(x)=0$ It has a root $c_{n}$ and only one in the interval $(0,1)$.
b) Calculate
$$
\lim_{n \rightarrow \infty} c_{n}
$$