Count how many of the numbers are odd. If an odd number of them are odd, then their sum is odd. If an even number of them are odd, then their sum is even.
You can work this out by realizing that the sum of the first x odd numbers is equal to x2.Consider the following examples:The first three odd numbers: 1 + 3 + 5 = 9The first five odd numbers: 1 + 3 + 5 + 7 + 9 = 25The first ten odd numbers: 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100In each case, the number of odds you're adding together is the square root of their sum. This means that the first 1500 consecutive odd numbers have a sum of 15002, which equals 2250000, or two and a quarter million.
The numbers are 15, 17, and 19.
Go through each of the numbers, and count how many of them are odd. If you count an odd number of them, then their sum is odd. If you count an even number of them, then their sum is even.
number of pairs of odd numbers whose sum is 32: 8pairs of odd numbers whose sum is 32:1, 313, 295, 277, 259, 2311, 2113, 1915, 17
The numbers are 13, 15 and 17.
The numbers are 17, 19, and 21.
They are: 13+15+17 = 45
13+15+17=45
17
Well, honey, all you need to do is check the last digit of each number. If there's an odd number of odd digits, the sum is odd. If there's an even number of odd digits, the sum is even. So, in this case, 13 and 17 are odd, and 45 and 24 are even, which means the sum is odd without adding them all up. Easy peasy, lemon squeezy!
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81