验证一个数是否是连续自然数的和

Question

/**
 * @Input: positive integer 
 * @Output: true if @Input is equal to
 * sum of all integers from 1 up to some n,
 * false otherwise
 *
 * @Example: 
 * isSum(10) = true as 10 = 1 + 2 + 3 + 4, 
 * isSum(14) = false
 */
function isSum(value) {

  var i = 1;  
  while (value > 0) {
    value -= i;
    i++;
  }
  if (!value) {
    return true;
  }
  return false;
}

这个function有问题吗？有没有更好的实现方法？

Answer 1

function isSum(value) {
    return Math.floor(Math.sqrt(value * 2)) * (Math.floor(Math.sqrt(value * 2)) + 1) / 2 == value;
}

Answer 2

用公式

1..n
(1 + n ) n / 2 = sum
function _is(num)
{
    result = false;
    for (i = 0; i < num; i++) {
       ((i + 1) * i) / 2 = sum
       if (sum == num) {
           result = true;
           break;
       }
       if (sum > num) {
          result = false;
          break
       }
    }
    return result
    }