Series Summation

• Write a function series_sum (or seriesSum, according to your language's case convention) that takes a 64-bit integer $n$ (you may assume $n \ge 1$ and returns the value

$$ \sum_{k=1}^{n} \frac{1}{k^2}. $$

• Use:

  • an integer for $n$,
  • a 64-bit floating point number for the return value.

• Boilerplate source files {go,jl,ml,rs}/series_sum.{go,jl,ml,rs} containing the test code is generated and shown below.

• Edit the source files either by opening them in a text editor (e.g., vscode), or editing the cells below and executing them.

Note

• As $n \rightarrow \infty$, the sum approaches

$$ \frac{\pi^2}{6}. $$

1. AI tutor

1-1. Prepare

• Your personal AI tutor is provided for questions and feedback
• Execute the following cell before you use it

import heytutor

1-2. Examples

1-2-1. A general question

%%hey
How to write a function in Go?

1-2-2. A hint on this specific problem

%%hey
Give me a hint on this problem for Rust

1-2-3. NEW: A few builtin variables

• {file:FILENAME} is the content of FILE
• {bash[-1]} is the output of the last %%bash_ cell, {bash[-2]} that of the second last %%bash_ cell, etc.
• {problem} is the content of the file you specified by %%hey problem_file=foo.md
• {answer} is the content of the file you specified by %%hey answer_file=go/foo.go

1-2-4. Help when you struggle

%%hey answer_file=go/foo.go
I get this error when I compile it. What's wrong?"

My program:
{answer}

Error message:
{bash[-1]}

1-2-5. Ask feedback

• You are encouraged to ask a feedback once you think you are done with the problem, to know if there is a better answer. You can do so by something like:

%%hey problem_file=foo.md answer_file=go/foo.md
Give me a feedback to my answer.

Problem:
{problem}

My Answer:
{answer}

2. Go

2-1. Baseline code

import heytutor

%%writefile_ go/series_sum.go
package main
import "math"
import "fmt"

/** begin my answer */

func seriesSum(n int64) float64 {
	sum := 0.0
	for k := int64(1); k <= n; k++ {
		x := float64(k)
		sum += 1.0 / (x * x)
	}
	return sum
}
/** end my answer */

func main() {
	a := math.Pi * math.Pi / 6.0
	if !(math.Abs(seriesSum(10) - 1.549768) < 1.0e-5) { panic("wrong") }
	if !(math.Abs(seriesSum(100000) - a) < 1.0e-5) { panic("wrong") }
	if !(math.Abs(seriesSum(1000000) - a) < 1.0e-6) { panic("wrong") }
	if !(math.Abs(seriesSum(20000000) - a) < 1.0e-6) { panic("wrong") }
	fmt.Println("OK")
}

2-2. Compile

%%bash_
export PATH=${PATH}:~/.local/go/bin:~/go/bin
go build -o go/series_sum go/series_sum.go

• Note: when you run go or other Go commands in a terminal (SSH or Jupyter terminal), you need to execute the first line (export PATH=${PATH}:~/go/bin)
• You may consider adding that line in your ~/.bash_profile

2-3. Run

%%bash_
go/series_sum

2-4. Ask Questions or Get Feedback

%%hey problem_file=series_sum.md answer_file=go/series_sum.go

Problem:
{problem}
My Answer (between /** begin my answer */ and /** end my answer */):
{answer}

Give me a feedback to my answer.

3. Julia

3-1. Baseline code

import heytutor

%%writefile_ jl/series_sum.jl
### begin my answer

function series_sum(n)
    s = 0.0
    for k in 1:n
        s += 1.0 / (k * k)
    end
    s
end
### end my answer

function main()
    a = pi * pi / 6.0
    @assert abs(series_sum(10) - 1.549768) < 1.0e-5
    @assert abs(series_sum(100000) - a) < 1.0e-5
    @assert abs(series_sum(1000000) - a) < 1.0e-6
    @assert abs(series_sum(20000000) - a) < 1.0e-6
    println("OK")
end

main()

3-2. Compile

• Julia code is compiled "just in time" (compiled upon executed), so does not need a specific action for compilation before you run

3-3. Run

%%bash_
export PATH=${PATH}:~/.juliaup/bin
julia jl/series_sum.jl

• Note: when you run julia or other Julia commands in a terminal (SSH or Jupyter terminal), you need to execute the first line (export PATH=${PATH}:~/.juliaup/bin)
• You may consider adding that line in your ~/.bash_profile

3-4. Interactive execution

• julia command also serves is an interactive command for Julia programs

• You can run a source code and continue interaction

$ julia -i jl/series_sum.jl

• For trial and error, you may also consider creating a Julia notebook

3-5. Ask Questions or Get Feedback

%%hey problem_file=series_sum.md answer_file=jl/series_sum.jl

Problem:
{problem}

My Answer (between ### begin my answer and ### end my answer):
{answer}

Give me a feedback to my answer.

4. OCaml

4-1. Baseline code

import heytutor

%%writefile_ ml/series_sum.ml
(** begin my answer *)

let series_sum n =
  let s = ref 0.0 in
  for k = 1 to n do
    let x = float_of_int k in
    s := !s +. 1.0 /. (x *. x)
  done;
  !s;;
(** end my answer *)

let main () =
  let a = Float.pi *. Float.pi /. 6.0 in
  (assert (abs_float (series_sum 10 -. 1.549768) < 1.0e-5);
   assert (abs_float (series_sum 100000 -. a) < 1.0e-5);
   assert (abs_float (series_sum 1000000 -. a) < 1.0e-6);
   assert (abs_float (series_sum 20000000 -. a) < 1.0e-6));
  Printf.printf "OK\n"
;;

main()

4-2. Compile

%%bash_
eval $(opam env)
ocamlc ml/series_sum.ml -o ml/series_sum

• Note: when you run ocamlc or other OCaml commands (see below) in a terminal (SSH or Jupyter terminal), you need to execute the first line (eval $(opam env))
• You may consider adding that line in your ~/.bash_profile

4-3. Run

%%bash_
ml/series_sum

4-4. Interactive execution

• ocaml command is an interactive command for OCaml programs

• In terminal (Jupyter or SSH), you can directly run a source code

$ eval $(opam env)   # once in your session or put it in ~/.bash_profile
$ ocaml ml/series_sum.ml

• You can run a source code and continue interaction

$ eval $(opam env)   # once in your session or put it in ~/.bash_profile
$ ocaml -init ml/series_sum.ml

• For trial and error, you may also consider creating an OCaml notebook

4-5. Ask Questions or Get Feedback

%%hey problem_file=series_sum.md answer_file=ml/series_sum.ml

Problem:
{problem}

My Answer (between (** begin my answer *) and (** end my answer *)):
{answer}

Give me a feedback to my answer.

5. Rust

5-1. Baseline code

import heytutor

%%writefile_ rs/series_sum.rs
/** begin my answer */

fn series_sum(n: i64) -> f64 {
    let mut sum = 0.0;
    for k in 1..=n {
        let x = k as f64;
        sum += 1.0 / (x * x);
    }
    sum
}
/** end my answer */

fn main() {
    let pi = std::f64::consts::PI;
    let a = pi * pi / 6.0;
    assert!((series_sum(10) - 1.549768).abs() < 1.0e-5);
    assert!((series_sum(100000) - a).abs() < 1.0e-5);
    assert!((series_sum(1000000) - a).abs() < 1.0e-6);
    assert!((series_sum(20000000) - a).abs() < 1.0e-6);
    println!("OK");
}

5-2. Compile

%%bash_
. ~/.cargo/env
rustc rs/series_sum.rs -o rs/series_sum

• Note: when you run rustc or other Rust commands in a terminal (SSH or Jupyter terminal), you need to execute the first line (. ~/.cargo/env)
• You may consider adding that line in your ~/.bash_profile

5-3. Run

%%bash_
rs/series_sum

5-4. Ask Questions or Get Feedback

%%hey problem_file=series_sum.md answer_file=rs/series_sum.rs

Problem:
{problem}

My Answer (between /** begin my answer */ and /** end my answer */):
{answer}

Give me a feedback to my answer.