x={1}; Do[ y = x[[k-1]]; AppendTo[x, y - (y^2-2)/(2*y)] , {k,2,10}] Out[6]= {1.0000000000000000000, 1.5000000000000000000, 1.4166666666666666667, > 1.4142156862745098039, 1.4142135623746899106, 1.4142135623730950488, > 1.4142135623730950488, 1.4142135623730950488, 1.4142135623730950488, > 1.4142135623730950488} Out[8]= 1.4142135623730950488 x={1.0000000000000000000000000000}; Do[ y = x[[k-1]]; AppendTo[x, y + (Cos[y]-y)/(Sin[y]+1)] , {k,2,10}]; N[x,20] In[21]:= Out[21]= {1.0000000000000000000, 0.75036386784024389303, > 0.73911289091136167036, 0.73908513338528396976, 0.73908513321516064166, > 0.73908513321516064166, 0.73908513321516064166, 0.73908513321516064166, > 0.73908513321516064166, 0.73908513321516064166} x={1.0000000000000000000000000000}; Do[ y = x[[k-1]]; AppendTo[x, y + (Cos[y]-2*y*Sin[y])/(3*Sin[y]+2*y*Cos[y])] , {k,2,10}]; N[x,20] n[24]:= Out[24]= {1.0000000000000000000, 0.68304185963654474091, > 0.65373187530249794484, 0.65327130479381105716, 0.65327118709441079158, > 0.65327118709440310111, 0.65327118709440310111, 0.65327118709440310111, > 0.65327118709440310111, 0.65327118709440310111} In[25]:= In[25]:= Cos[x]-2 x Sin[x] Out[25]= {-1.142639663747653295904068036, -0.086554662528006831748788342, -7 > -0.00131831390222452941817348, -3.3672473157863869973 10 , -14 -25 -25 -25 -25 -24 > -2.200156433865 10 , 0. 10 , 0. 10 , 0. 10 , 0. 10 , 0. 10 }