I have two IVP ODE's that i can find the approximate solutions of but I cant figure out how to plot them correctly

for the first one i have tried this..

it needs to be plotted on the interval [1,4]

> with(plots);
> plot((-1)-1+x+(1/2)*(-1+x)^2+(-1+x)^3+(2/3)*(-1+x)^4+(37/60)*(-1+x)^5+(127/360)*(-1+x)^6+(31/140)*(-1+x)^7+(185/2016)*(-1+x)^8+(53/1620)*(-1+x)^9-(391/151200)*(-1+x)^10-(1097/90720)*(-1+x)^11-(160903/11975040)*(-1+x)^12-(969289/97297200)*(-1+x)^13-(4366883/681080400)*(-1+x)^14-(5242229/1513512000)*(-1+x)^15+O((-1+x)^16), x = 1 .. 4);