SeriesSum

program SeriesSum;

{$APPTYPE CONSOLE}

uses
  SysUtils;

function LnOneMinusX(X: Real; Eps: Real; var N: Integer): Real;
var
  R: Real;
  Sum: Real;
  Numerator, Denominator: Real;
begin
  N := 0;
  Sum := 0;
  R := 1;
  Numerator := 1;
  Denominator := 0;
  while Abs(R) > Eps do
  begin
    Numerator := Numerator * X;
    Denominator := Denominator + 1;
    R := Numerator / Denominator;
    Sum := Sum - Numerator / Denominator;
    Inc(N);
  end;
  Result := Sum;
end;

var
  Eps: Real;
  X: Real;
  N: Integer;
  EpsValue: Real;
  PreciseValue: Real;

begin
  Write('Enter X (from 0 to 1), Eps: ');
  ReadLn(X, Eps);

  EpsValue := LnOneMinusX(X, Eps, N);
  PreciseValue := Ln(1 - X);
  WriteLn;
  WriteLn('Step count: ', N);
  WriteLn('Ln(1 - X) = ', EpsValue:14:11, ' (with Eps: ', Eps, ')');
  WriteLn('Ln(1 - X) = ', PreciseValue:14:11, ' (precise)');
  WriteLn('Absolute error: ', Abs(PreciseValue - EpsValue):14:11);
  WriteLn('Relative error: ', Abs((PreciseValue - EpsValue) / PreciseValue):14:11);

  Readln;
end.