Sum the first N numbers in java

Question

Hello, I am new to programming and I am trying to write a small program where it will calculate the sum for first N numbers. The problem is it does not work for even numbers. I have not managed to figure out why. My code is as follow:

int n = Integer.parseInt(args[0]);
    int sum = (1+n)/2*n;
    System.out.println(sum + " is the sum of first " + n + " numbers");

Answer 1

It doesn't work for even n because (n+1)/2 is truncated to an int.

This means that if, for example, n=4 , (n+1)/2 results in 2 instead of 2.5, so when you multiply it by n, you get 8 instead of the desired 10.

You can overcome this problem simply by changing the order of the operations. If you first multiply n by (n+1), the result is guaranteed to be even, so dividing it by 2 will produce the correct answer.

int sum = n*(1+n)/2;

Answer 2

You have integer division with (1+n)/2 . If your number is even, then (1+n) is odd and the division by 2 will truncate any decimal result, so that an int divided by an int is still an int .

Multiply by n first, then divide by 2 . This ensures that the product is even before dividing, so the result is correct.

int sum = (1+n) * n / 2;

Answer 3

One can use ((n * (n + 1)) / 2) . But I think the following will work without overflow errors for a few additional values of n :

if ((n & 1) == 0) {
  sum = ((n >> 1) * (n + 1));
} else {
  sum = (n * ((n + 1) >> 1));
}