Вычислить значение суммы

program Vych_8;
var n,x:integer;
function sum(k:integer):extended;
begin
if k=1 then sum:=x
else
begin
sum:=sum(k-1);
sum:=sum+exp((2*k-1)*ln(x))/(2*k-1);
end;
end;
begin
repeat
writeln('x= '); readln(x);
writeln('n= '); readln(n);
until (x>=-100) and (x<=10000) and (n>0) and (n<=100);
writeln('x = ',x,' n = ',n);
writeln('s=',sum(n):0:3);
readln;
end.

function p(x : Real; n : Integer) : Real;
begin
  if n = 0 then
    p := 1
  else if odd(n) then
    p := x * p(x, n - 1)
  else
    p := sqr(p(x, n shr 1))
end;
 
function s(x : Real; n : Integer) : Real;
begin
  if n = 1 then
    s := x
  else
    s := ( s(x, n-1) * (2*n-1) + p(x, 2*n-1) ) / (2*n-1)
end;
 
var
  x : Real;
  n : Integer;
begin
  Read(x, n);
  WriteLn(s(x, n):0:7);
end.

var n,i:integer;
    x,t,s:real;
begin
repeat
write('Введите |x|<1 x= ');
readln(x);
until abs(x)<1;
repeat
write('Введите n>0 n= ');
readln(n);
until n>0;
t:=x;
s:=t;
for i:=2 to n do
 begin
  t:=t*x*x;
  s:=s+t/(2*i-1);
 end;
writeln('S=',s:0:4);
write('arth(x)=',0.5*ln((1+x)/(1-x)):0:4)
end.

function sum_recursive(x, xk: real; k, n: integer): real;
begin
  if k = 2 * n - 1 then sum_recursive := xk / k
  else sum_recursive := sum_recursive(x, xk * x * x, k + 2, n) + xk / k
end;
 
var
  x: real;
  n: integer;
begin
  x := 0.7;
  n := 10;
  writeln('    S(x) = ', sum_recursive(x, x, 1, n) :0:15);
  writeln('arcth(x) = ', ln((1 + x) / (1 - x)) / 2 :0:15);
  readln
end.

function sum_recursive(x: real; n: integer): real;
  function recursive(xk: real; k, kmax: integer): real;
  begin
    if k = kmax then recursive := xk / k
    else recursive := recursive(xk * x * x, k + 2, kmax) + xk / k
  end;
begin
  sum_recursive := recursive(x, 1, 2 * n - 1)
end;
 
var
  x: real;
  n: integer;
begin
  x := 0.7;
  n := 10;
  writeln('    S(x) = ', sum_recursive(x, n) :0:15);
  writeln('arcth(x) = ', ln((1 + x) / (1 - x)) / 2 :0:15);
  readln
end.

function sum_recursive(x, xk: real; k, n: integer): real;
begin
  if k = 2 * n - 1 then sum_recursive := xk / k
  else sum_recursive := sum_recursive(x, xk * x * x, k + 2, n) + xk / k
end;
 
function sum_iterative(x: real; n: integer): real;
var
  s, xk: real;
  k, kmax: integer;
begin
  xk := x;
  s := 0;
  k := 1;
  kmax := 2 * n - 1;
  while k <= kmax do
    begin
      s := s + xk / k;
      xk := xk * x * x;
      inc(k, 2)
    end;
  sum_iterative := s
end;
 
var
  x: real;
  n: integer;
begin
  repeat
    write('|x| < 1; x = ');
    readln(x)
  until abs(x) < 1;
  repeat
    write('n > 0; n= ');
    readln(n)
  until n > 0;
  writeln('     Сумма рекурсивно: ', sum_recursive(x, x, 1, n) :0:15);
  writeln('     Сумма итеративно: ', sum_iterative(x, n) :0:15);
  writeln('arcth(x) аналитически: ', ln((1 + x) / (1 - x)) / 2 :0:15);
  readln
end.

function recursive(x, xk: real; k, kmax: integer): real;
begin
  if k = kmax then recursive := xk / k
  else recursive := recursive(x, xk * x * x, k + 2, kmax) + xk / k
end;
 
function sum_recursive(x: real; n: integer): real;
begin
  sum_recursive := recursive(x, x, 1, 2 * n - 1)
end;

function sum_recursive(x: real; n: integer): real;
var
  kmax: integer;
  function recursive(xk: real; k: integer): real;
  begin
    if k = kmax then recursive := xk / k
    else recursive := recursive(xk * x * x, k + 2) + xk / k
  end;
begin
  kmax := 2 * n - 1;
  sum_recursive := recursive(x, 1)
end;