Sample 1.  Find a root of f(x) = x**5 - 3x**4 + x**3 - 4x**2 + x - 6 = 0.


 Iteration       Newton Approximation

         0       3.120000000000000000000000000000000000000000000000000000000000

         1       3.120656718532108533919391265947916793506741449899073468862023

         2       3.120656215327022122238354686569835883519704471397219749798884

         3       3.120656215326726500470956115551705969611230193197937042123082

         4       3.120656215326726500470956013523797484654623935599078168006617

         5       3.120656215326726500470956013523797484654623935599066014988828

         6       3.120656215326726500470956013523797484654623935599066014988828



 Sample 2.          109 terms were added

 Zeta(3) =    1.202056903159594285399738161511449990764986292340498881792272



 Sample 3.           22 values were tested

 p =   1000000000000000000000000000000000000000000000000000000000000000659661


 All results were ok.