# 10.1 Limits of Sequences # Art Belmonte, Summer 1996 # These are the shaded gray examples which appear in Section 10.1. # (These commands actually precede Section 10.1.) > restart; a:=n->1/n^2; seq(a(n), n=5..9); 1 a := n -> ---- 2 n 1/25, 1/36, 1/49, 1/64, 1/81 # Note also that the index variable n is explicitly unassigned after the # sequence has been constructed. This is new in Release 4. > b:=n->(2*n-1) / (3*n+6); disp:=seq([n, b(n)], n=1..50): n; 2 n - 1 b := n -> ------- 3 n + 6 n # Here we use symbol=POINT to better distinguish individual elements of # the sequence when they start clustering. > plot([disp], style=point, symbol=POINT); > Limit(b(n), n=infinity); value("); 2 n - 1 lim ------- n -> infinity 3 n + 6 2/3 >