Harmonic series: Difference between revisions
Add C# implementation
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end</syntaxhighlight>
=={{header|C#}}==
{{trans|Go}}
<syntaxhighlight lang="C#">
using System;
using System.Numerics;
public class BigRational
{
public BigInteger Numerator { get; private set; }
public BigInteger Denominator { get; private set; }
public BigRational(BigInteger numerator, BigInteger denominator)
{
if (denominator == 0)
throw new ArgumentException("Denominator cannot be zero.", nameof(denominator));
BigInteger gcd = BigInteger.GreatestCommonDivisor(numerator, denominator);
Numerator = numerator / gcd;
Denominator = denominator / gcd;
if (Denominator < 0)
{
Numerator = -Numerator;
Denominator = -Denominator;
}
}
public static BigRational operator +(BigRational a, BigRational b)
{
return new BigRational(a.Numerator * b.Denominator + b.Numerator * a.Denominator, a.Denominator * b.Denominator);
}
public override string ToString()
{
return $"{Numerator}/{Denominator}";
}
}
class Program
{
static BigRational Harmonic(int n)
{
BigRational sum = new BigRational(0, 1);
for (int i = 1; i <= n; i++)
{
BigRational r = new BigRational(1, i);
sum += r;
}
return sum;
}
static void Main(string[] args)
{
Console.WriteLine("The first 20 harmonic numbers and the 100th, expressed in rational form, are:");
int[] numbers = new int[21];
for (int i = 1; i <= 20; i++)
{
numbers[i - 1] = i;
}
numbers[20] = 100;
foreach (int i in numbers)
{
Console.WriteLine($"{i,3} : {Harmonic(i)}");
}
Console.WriteLine("\nThe first harmonic number to exceed the following integers is:");
const int limit = 10;
for (int i = 1, n = 1; i <= limit; n++)
{
double h = 0;
for (int j = 1; j <= n; j++)
{
h += 1.0 / j;
}
if (h > i)
{
Console.WriteLine($"integer = {i,2} -> n = {n,6} -> harmonic number = {h,9:F6} (to 6dp)");
i++;
}
}
}
}
</syntaxhighlight>
{{out}}
<pre>
The first 20 harmonic numbers and the 100th, expressed in rational form, are:
1 : 1/1
2 : 3/2
3 : 11/6
4 : 25/12
5 : 137/60
6 : 49/20
7 : 363/140
8 : 761/280
9 : 7129/2520
10 : 7381/2520
11 : 83711/27720
12 : 86021/27720
13 : 1145993/360360
14 : 1171733/360360
15 : 1195757/360360
16 : 2436559/720720
17 : 42142223/12252240
18 : 14274301/4084080
19 : 275295799/77597520
20 : 55835135/15519504
100 : 14466636279520351160221518043104131447711/2788815009188499086581352357412492142272
The first harmonic number to exceed the following integers is:
integer = 1 -> n = 2 -> harmonic number = 1.500000 (to 6dp)
integer = 2 -> n = 4 -> harmonic number = 2.083333 (to 6dp)
integer = 3 -> n = 11 -> harmonic number = 3.019877 (to 6dp)
integer = 4 -> n = 31 -> harmonic number = 4.027245 (to 6dp)
integer = 5 -> n = 83 -> harmonic number = 5.002068 (to 6dp)
integer = 6 -> n = 227 -> harmonic number = 6.004367 (to 6dp)
integer = 7 -> n = 616 -> harmonic number = 7.001274 (to 6dp)
integer = 8 -> n = 1674 -> harmonic number = 8.000486 (to 6dp)
integer = 9 -> n = 4550 -> harmonic number = 9.000208 (to 6dp)
integer = 10 -> n = 12367 -> harmonic number = 10.000043 (to 6dp)
</pre>
=={{header|C++}}==
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