求調和級數(harmonics)之和


[code delphi]
{ 調和級數之和, 以最簡分數表示
1 1 1
H(n) = 1 - - ... -
2 3 n
}
program sumHarmonic;
{$APPTYPE CONSOLE}
uses
SysUtils;
const
firstterm = 2;
var
numerator, denominator,
lastterm, termcount : integer;
{ Divide num and den by their GCD. }
procedure lowterm(var num, den :integer);
var
numcopy, dencopy, remainder : integer;
begin
numcopy:=num;
dencopy:=den;
while dencopy<>0 do
begin
remainder := numcopy mod dencopy;
numcopy := dencopy;
dencopy := remainder;
end;
if numcopy > 1 then
begin
num := num div numcopy;
den := den div numcopy;
end;
end; { lowterm }
{ Calculate the exact sum of two rational numbers }
procedure addrationals(var num1, den1:integer;
num2, den2 : integer);
begin
num1:=num1 * den2 num2 * den1;
den1:=den1 * den2;
end;
begin { sumHarmonics }

numerator :=1;
denominator:=1;
read(lastterm);
for termcount:=firstterm to lastterm do
begin
addrationals(numerator, denominator, 1, termcount);
lowterm(numerator, denominator);
writeln(numerator:4 , ' / ', denominator:4)
end;
end. { sumHarmonics }

[/code]

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