31. To prove that the sum of the interior angles of a convex N-sided polygon on a plane is $(2 N-5) \cdot 180^{\circ} (N>2)$. Below is an incorrect proof, and the first error is ( ).
(A) Step one: For $k=3$, the polygon is a triangle, and the sum of the three interior angles of a triangle is $180^{\circ}$, which is $(2 \times 3-5) \cdot 180^{\circ}$ $=180^{\circ}$
(B) Step two: Let $k$ be a fixed positive integer greater than 3, assume that the sum of the interior angles of a convex $k$-sided polygon is $(2 k-5) \cdot 180^{\circ}$
(C) Step three: For a convex $(k+1)$-sided polygon, we can choose two vertices and connect them with a line segment, dividing it into a convex $k$-sided polygon and a triangle
(D) Step four: The sum of the interior angles of a $(k+1)$-sided polygon is $[2(k+1)-5] \cdot 180^{\circ}$
(E) Step five: By mathematical induction, for any integer $N>2$, the sum of the interior angles of a convex $N$-sided polygon is $[2 N-5] \cdot 180^{\circ}$