​

// factorial with for loop... 

// start with while loop

// comment it out (keep it for comparison purposes)

// below the comment, refactor the program as a for loop

​

// exercise: termial with for loop vs closed formula

​

let sum = 0;

let n = 10 ** 8;

​

for (let k = 1; k <= n; k++) {

  sum += k;

}

​

// on my machine, the for loop breaks at n = 10 ** 9

// (it runs for a while, then returns the wrong answer)

console.log(sum);

console.log(n * (n + 1) / 2);

​

/* Bonus exercise: 

Determine the precise threshold where the termial breaks! Can use a variation

of the bisection method that we introduced, called binary search. 

​

The difference is that we're searching a discrete range of values, like 1000, 1001,

10002..., 10 **9 rather than a continuous range of values, like the decimal numbers

between 0 and 1. 

​

If multiple people try this, we'll have a collective experiment to see if the

result depends on the computer that's running the code!

​

Note to self: 

I should do this myself, in case there are any hints I want to provide

(I could provide them in a separate file), and to make sure the concepts that

are used are all things we've covered so far. Also, would this work? The problem

is that when a value is too big, it'll break the function...

*/