I just can’t understand the lesson “Replace loops using recursion” of freeCodeCamp. I’ll quote that part below;

Recursion is the concept that a function can be expressed in terms of itself. To help understand this, start by thinking about the following task: multiply the first n elements of an array to create the product of those elements. Using a for loop, you could do this:

function multiply(arr, n) { var product = 1; for (var i = 0; i < n; i++) { product *= arr[i]; } return product; }However, notice that

multiply(arr, n) == multiply(arr, n – 1) * arr[n – 1]. That means you can rewrite multiply in terms of itself and never need to use a loop.function multiply(arr, n) { if (n <= 0) { return 1; } else { return multiply(arr, n - 1) * arr[n - 1]; } }

Especially this part.
**multiply(arr, n) == multiply(arr, n – 1) * arr[n – 1]**

I can understand if it’s like this;

multiply(arr, n) == multiply(arr, n – 1) * **arr[n]**

That’s because if arr = [2,3,4,5,6,7,8,9],

multiply(arr, 5); equals 2*3*4*5*6*7

multiply(arr, 4); equals 2*3*4*5*6

multiply(arr, 4) * arr[5]; equals (2*3*4*5*6)*7

So `multiply(arr, n)`

and `multiply(arr, n - 1) * arr[n]`

is the same value”

However, I can’t understand why **multiply(arr, n) == multiply(arr, n – 1) * arr[n – 1]** ?
Can anyone please tell what’s happening in this code? Why they are equal?

## Answer

`However, I can't understand why multiply(arr, n) == multiply(arr, n - 1) * arr[n - 1] ? Can anyone please tell what’s happening in this code? Why they are equal?`

The given algorithm is multiplying the first `n`

elements of an array `arr`

and returning the answer.

Now, to multiply the first `n`

elements, we can multiply the first `(n-1)`

elements and then multiply the result with the `n`

th element of the array.

So, `multiply(arr, n) == multiply(arr, n - 1) * arr[n - 1]`

.

`multiply(arr, n)`

means multiply the first `n`

elements of the array `arr`

.

`multiply(arr, n - 1)`

means multiply the first `n-1`

elements of the array `arr`

.