Compute the   nth   term of a series,   i.e. the sum of the   n   first terms of the corresponding sequence.

Informally this value, or its limit when   n   tends to infinity, is also called the sum of the series, thus the title of this task.

For this task, use:

 




S

n


=

∑

k
=
1


n




1

k

2






{\displaystyle S_{n}=\sum _{k=1}^{n}{\frac {1}{k^{2}}}}




 and compute   




S

1000




{\displaystyle S_{1000}}




This approximates the   zeta function   for   S=2,   whose exact value

 



ζ
(
2
)
=



π

2


6




{\displaystyle \zeta (2)={\pi ^{2} \over 6}}


is the solution of the Basel problem.




const LOWER: i32 = 1;
const UPPER: i32 = 1000;
 
// Because the rule for our series is simply adding one, the number of terms are the number of
// digits between LOWER and UPPER
const NUMBER_OF_TERMS: i32 = (UPPER + 1) - LOWER;
fn main() {
    // Formulaic method
    println!("{}", (NUMBER_OF_TERMS * (LOWER + UPPER)) / 2);
    // Naive method
    println!("{}", (LOWER..UPPER + 1).fold(0, |sum, x| sum + x));
}
 