(* Here is the true solution to our differential equation y'=1-y: *) 
Clear[h]
y[i_]:=1-Exp[-i*h]
(* Here is the Euler approximate solution: *) 
w[i_]:=If[i>0,(*then*) h+(1-h)w[i-1],(*else*) 0]

Table[Series[y[i],{h,0,5}],{i,0,10,2}]//TableForm

Table[Expand[w[i]],{i,0,10,2}]//TableForm

ww[i_]:=If[i>0,h(1-h/2)+(1-h+h^2/2)ww[i-1],0]

Table[Expand[ww[i]],{i,0,10,2}]//TableForm

www[i_]:=If[i>0,h(1-h/2+h^2/6)+(1-h+h^2/2+h^3/6)www[i-1],0]

Table[Expand[www[i]],{i,0,10,2}]//TableForm

n=10
h=1/n
ListPlot[{Table[y[i],{i,0,n}],Table[w[i],{i,0,n}]}]