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size(200,200,IgnoreAspect);
import graph;
real L=1;
real epsilon=0.25;
real a(int n) {return L+1/n;}
for(int i=1; i < 20; ++i)
dot((i,a(i)));
real N=1/epsilon;
xaxis(Label("$n$",align=2S));
yaxis(Label("$a_n$",0.85));
xtick("$2$",2);
ytick("$\frac{3}{2}$",3/2);
ytick("$2$",2);
yequals(Label("$L$",0,up),L,extend=true,blue);
yequals(Label("$L+\epsilon$",1,NW),L+epsilon,extend=true,red+dashed);
yequals(Label("$L-\epsilon$",1,SW),L-epsilon,extend=true,red+dashed);
xequals(N,extend=true,darkgreen+dashed);
labelx(shift(0,-10)*"$N=\frac{1}{\epsilon}$",N,E,darkgreen);
label("$a_n=1+\frac{1}{n},\quad \epsilon=\frac{1}{4}$",point((0,1)),10S+E);
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