PLEASE ANSWER #$14$

Prove that the $n$ points of Problem $12$ form a convex segment.

Consider $n$ points $p_i=(i,\frac{i(i-1)}{2})inZZ,$ where $p_{i-1},p_i{L}_i{L}_1,L_5,L_{10}{L}_{i}1i,$ let points

$p_{i-1},p_i$ define line segment $L_i.$

What are the slopes $of{L}_1,L_5,L_{10}?In$ general, what $is$ the slope $of{L}_i?0i.$ For $1i,$ let points

$p_{i-1},p_i$ define line segment $L_i.$

What are the slopes $of{L}_1,L_5,L_{10}?In$ general, what $is$ the slope $of{L}_i?$