Finding the sum of all the multiples of 3 or 5 below any given number
I'm going to take by "shorten", you mean "remove this duplication", in which case the answer is yes. Extract an SumSequence function. Give things some breathing space while you're at it.

function sum_of_all_mul_3_5(){
    var value=parseInt(document.getElementById("input").value);
    var result=sumSequence(value, 3) + sumSequence(value, 5) - sumSequence(value, 15);
    document.getElementById("output").value=result ;
    }

function sumSequence(value, x){
    return (Math.floor((value - 1) / x) * (x + ((Math.floor(value - 1) / x) * x))) / 2);
    }


For the record though, using the arithmetic sum of the sequence is a very elegant solution to this problem though. I know of no more efficient way to do it, but a comment explaining what's going on here would be beneficial to any future maintainer. You might even want to go the extra mile and drop a link to wikipedia in that comment.