All right, first we need to write this in an understandable fashion. I assume you mean a sum of an odd number of odd numbers. We can write such a sum in this fashion...
SUM from i=1 to i=2n+1 of (2i+1)
Now, this can be proven to be equal to 4n2+8n+3 for some integer n. Now, doing a quick factorization, we see that this is equal to (2n+1)(2n+3), again, for integer n. Since the left side of the product (2n+1) is odd, and the right side of the product (2n+3) is also odd, we can see that (2n+1)(2n+3), being the product of two odd numbers, is also odd. Thus, the sum of any odd amount of odd numbers will also be odd.
The sum of two odd numbers is always an even number, e.g. 3 + 5 =8. This can be proven as follows:
Every even number can be expressed as 2m where m is a real number.
Every odd number can therefore be expressed as 2m+1 where m is a real number.
For this proof, we will consider two different odd numbers: 2m+1 and 2k+1.
2m+1 + 2k+1
=2m + 2k + 2
=2(m + k + 1)
As m+k+1 is a real number, the answer must be even. Therefore the sum of any two odd numbers is an even number.
All of them? If you include negative numbers then zero, as every positive number has a negative that will cancel it out. If you mean only positive numbers then it is infinity.
The sum of nth odd number can be calculated by S(n+1) = (n+1)(n+2)/2
1+3+5+7+9 = 25
16
The sum of all odd numbers 1 to 120,000 is 14,400,000,000.
The sum of all the odd numbers between 1 and 12000 is 36000000.
The sum of all odd numbers from 1 to 64 inclusive is 4,096
The sum of the first 500 odd numbers is 250,000.
The sum of all the odd numbers from 1 through 100 is 10,000
The sum of all odd numbers 1 through 99 is 9,801.
The sum of two odd numbers is always even; the sum of three odd numbers is always odd; the sum of four odd numbers is always even; the sum of five odd numbers is always odd; etc
If this question means "in the interval 0 to 16 inclusive, is the sum of the odd numbers the same as the sum of the even numbers ?" then the answer is no. The sum of the even numbers is eight more than the sum of the odd ones.
The answer is zero !
The sum of an odd number of odd numbers will be odd.
The sum is 10,000
No. Odd numbers can be written as the sum of consecutive integers, but some multiples of odd numbers are even.