int i = 0;                            // array starts from 0
int [] array = new int[100];          // create larger array
while(i < array.length && sum <= 100) // i should be less then length
                                      // && instead of ||
{
   System.out.println("Write in the " + i + " number") ; 
   array[i] = input.nextInt();
   sum += array[i];                   // += instead of =+
   System.out.println("sum is " + sum);
   i++;                               // increment i 
}  

Ideone DEMO

This is better done using a for each loop:

for(String x:studentArray){
  // do what you want to do with x
}

To skip over values that are null, just insert an if check at the beginning of the loop and continue if x is empty.

The better question might be: Why wouldn't you want to use a FOR loop to iterate through an array? There are many ways to iterate through an Array or a collection and there is no law that states you have to use the FOR loop. In a lot of cases, it's simply the best to use for speed, ease of use, and readability. And yet, in other cases it is not:

The Array:

int[] array = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10};

Display Array with the typical for loop:

for (int i = 0; i < array.length; i++) {
    System.out.println(array[i]);
}

Display Array with the enhanced for loop:

for(Integer num : array) {
    System.out.println(num);
}

Display Array with the do/while loop:

int i = 0;
do {
    System.out.println(array[i++]);
} while (i < array.length);

Display Array with the while loop:

int j = 0;
while (j < array.length) {
    System.out.println(array[j++]);
}

Display Array through Recursive Iteration:

iterateArray(array, 0);  // 0 is the start index.


// The 'iterateArray()' method:
private static int iterateArray(int[] array, int index) {
    System.out.println(array[index]);
    index++; 
    if (index == array.length) {
        return 0;
    }
    return iterateArray(array,index);
}

Display Array using Arrays.stream() (Java8+):

Arrays.stream(array).forEach(e->System.out.print(e + System.lineSeparator())); 

Display Array using IntStream (Java8+):

IntStream.range(0, array.length).mapToObj(index -> array[index]).forEach(System.out::println);

Choose your desired weapon....

You are incrementing the counter too early, because of that in the last iteration it has the value myArray.length

Move location++ at the end of the loop, or use a for loop