Harmonic series: Difference between revisions

</pre>

=={{header|Rust}}==

Using big rationals.

<lang rust>

use num::rational::Ratio;

use num::{BigInt, FromPrimitive};

fn main() {

for n in 1..=20 {

println!("Harmonic number {} = {}", n, harmonic_number(n.into()));

}

println!("Harmonic number 100 = {}", harmonic_number(100.into()));

let max = 5;

let mut target = 1;

let mut i = 1;

while target <= max {

if harmonic_number(i.into()) > Ratio::from_integer(FromPrimitive::from_u64(target).unwrap())

{

println!("Position of first term > {} is {}", target, i);

target += 1;

}

i += 1;

}

}

fn harmonic_number(n: BigInt) -> Ratio<BigInt> {

let mut result: Ratio<BigInt> = Ratio::from_integer(FromPrimitive::from_u8(0).unwrap());

let mut i: BigInt = FromPrimitive::from_u8(1).unwrap();

let one: Ratio<BigInt> = Ratio::from_integer(FromPrimitive::from_u8(1).unwrap());

while i <= n {

result = &result + &one / &i;

i += 1;

}

result

}

</lang>

{{out}}

<pre>

Harmonic number 1 = 1

Harmonic number 2 = 3/2

Harmonic number 3 = 11/6

Harmonic number 4 = 25/12

Harmonic number 5 = 137/60

Harmonic number 6 = 49/20

Harmonic number 7 = 363/140

Harmonic number 8 = 761/280

Harmonic number 9 = 7129/2520

Harmonic number 10 = 7381/2520

Harmonic number 11 = 83711/27720

Harmonic number 12 = 86021/27720

Harmonic number 13 = 1145993/360360

Harmonic number 14 = 1171733/360360

Harmonic number 15 = 1195757/360360

Harmonic number 16 = 2436559/720720

Harmonic number 17 = 42142223/12252240

Harmonic number 18 = 14274301/4084080

Harmonic number 19 = 275295799/77597520

Harmonic number 20 = 55835135/15519504

Harmonic number 100 = 14466636279520351160221518043104131447711/2788815009188499086581352357412492142272

Position of first term > 1 is 2

Position of first term > 2 is 4

Position of first term > 3 is 11

Position of first term > 4 is 31

Position of first term > 5 is 83