Chapter 5 - Section 5.7 - Factoring by Special Products - Exercise Set - Page 310: 86

$c=1$

The third term of a perfect square trinomial is equal to the square of half of the coefficient of the middle term. Hence, to make the given expression, $ n^2-2n+c $, a perfect square trinomial, then, \begin{array}{l} c=\left( \dfrac{-2}{2} \right)^2 \\\\ c=\left( -1 \right)^2 \\\\ c=1 .\end{array}