Re: what did I do wrong here ?

let me try to explain the function another way.

It does not work as you explained, but the other way (from n to 0).

```ocaml
let rec sum = function
| 0 -> 0
| n -> n + sum(n - 1)
```

sum 3 is replaced by
3 + sum 2 which is replaced by
3 + 2 + sum 1 which is replaced by
3 + 2 + 1 + sum 0 whis is replaced by
3 + 2 + 1 + 0

The factorial function you showed is also working this way.

We can try to go the other way…

```ocaml
let sum n =

    (* we hide a func inside *)
    let rec embeded_sum step result =
        if step = n                            (* when  n is reached *)
        then result + n                     (* finish with the final 
result by summing the previous one with n *)
        else sum (step + 1) (step + result) in   (* else, increment the 
result with step, and go to the next one *)

    embeded_sum 0 0      (* start from 0, with the result 0 *)
````

Here are the values of step and result.

step           result
0                0
1                0
2                1
3                3
4                6
5                10
...

-- 
Matthieu Dubuget
Guide d’autodéfense numérique : http://guide.boum.org