find the sum of the multiples of 3 and 5 below 1000

Question

Ok guys, so I\'m doing the Project Euler challenges and I can\'t believe I\'m stuck on the first challenge. I really can\'t see why I\'m getting the wrong answer despite my

Answer 1

Don't you all think instead of using loops to compute the sum of multiples, we can easily compute sum of n terms using a simple formula of Arithmetic Progression to compute sum of n terms.

I evaluated results on both using loop and formula. Loops works simply valuable to short data ranges. But when the data ranges grows more than 10¹⁰ program takes more than hours to process the result with loops. But the same evaluates the result in milliseconds when using a simple formula of Arithmetic Progression.

What we really need to do is:
Algorithm :

1. Compute the sum of multiples of 3 and add to sum.
2. Compute the sum of multiples of 5 and add to sum.
3. Compute the sum of multiples of 3*5 = 15 and subtract from sum.

Here is code snippet in java from my blog post CodeForWin - Project Euler 1: Multiples of 3 and 5

n--; //Since we need to compute the sum less than n.
//Check if n is more than or equal to 3 then compute sum of all divisible by
//3 and add to sum.  
if(n>=3) {  
    totalElements = n/3;  
    sum += (totalElements * ( 3 + totalElements*3)) / 2;  
}  

//Check if n is more than or equal to 5 then compute sum of all elements   
//divisible by 5 and add to sum.  
if(n >= 5) {  
    totalElements = n/5;  
    sum += (totalElements * (5 + totalElements * 5)) / 2;  
}  

//Check if n is more than or equal to 15 then compute sum of all elements  
//divisible by 15 and subtract from sum.  
if(n >= 15) {  
    totalElements = n/15;  
    sum -= (totalElements * (15 + totalElements * 15)) / 2;  
}  

System.out.println(sum);