program ex1_14

  implicit none

  real(8) e1,er,a(10),b(10),s

  integer n

  
e1=exp(1.0d0)

  write(*,*)'e = ',e1


  a(1)=1.0d0

  do n=1,9

     a(n+1)=a(n)*dble(n+1)

  enddo

  do n=1,10

     b(n)=1.0d0/a(n)

  enddo

  s=1.0d0

  write(*,*)'n,s,er',1,s,abs(e1-s)

  do n=2,10

     s=s+b(n-1)

     write(*,*)'n,s,er',n,s,abs(e1-s)

  enddo
end program ex1_14




output
 e =    2.7182818284590451
 n,s,er           1   1.0000000000000000        1.7182818284590451
 n,s,er           2   2.0000000000000000       0.71828182845904509
 n,s,er           3   2.5000000000000000       0.21828182845904509
 n,s,er           4   2.6666666666666665       5.16151617923785722E-002

 n,s,er           5   2.7083333333333330       9.94849512571205352E-003

 n,s,er           6   2.7166666666666663       1.61516179237874979E-003

 n,s,er           7   2.7180555555555554       2.26272903489643795E-004

 n,s,er           8   2.7182539682539684       2.78602050767240428E-005

 n,s,er           9   2.7182787698412700       3.05861777505356258E-006

 n,s,er          10   2.7182815255731922       3.02885852843104431E-007