const e=0.001;
var a,b,h,x,r,s,y:real; n,i,k:integer;
begin
write('a=');readln(a);
write('b=');readln(b);
h:=0.1;
x:=a-h;
n:=round((b-a)/h)+1;
writeln(' №   x     S(x)     y(x)       погрешность');
for i:=1 to n do
begin
 x:=x+h;
 r:=8*sqrt(x)*x/6; s:=r; k:=1;
 while abs(r)>e do begin
 inc(k);
 r:=r*k*x/(2*(2*k+1)*(k-1)*(k-1));
 s:=s+r;
 end;
 y:=(x+1-sqrt(x))*exp(sqrt(x))-(x+1+sqrt(x))*exp(-sqrt(x));
 writeln(i:2,'  ',x:3:1,' ',s:8:4,' ',y:8:4,'  ',abs(s-y));
 end;
end.

Пример:
a=1
b=2
 №   x     S(x)     y(x)       погрешность
 1  1.0   1.6146   1.6146  5.05697293706753E-06
 2  1.1   1.8972   1.8972  8.54973897013167E-06
 3  1.2   2.2012   2.2012  1.38099640434319E-05
 4  1.3   2.5271   2.5271  2.56691048861057E-07
 5  1.4   2.8751   2.8751  4.15808958376118E-07
 6  1.5   3.2456   3.2456  6.51534709295021E-07
 7  1.6   3.6390   3.6390  9.91761193169793E-07
 8  1.7   4.0556   4.0556  1.47173002851275E-06
 9  1.8   4.4960   4.4960  2.13532739756772E-06
10  1.9   4.9605   4.9605  3.03650996258398E-06
11  2.0   5.4496   5.4496  4.24086530514955E-06