the sum of an odd number of odd terms is?

Answer 1

try answering this yourself... for example, consider the situation when there is only one (one is an odd number) odd term....
Now, note, that whether you have 3, 5 or 353 terms, the answer must be the same, as long as the question is correct.

Answer 2

The sum of an odd number of odd terms is odd.

First, confirm that an odd number plus an even number is odd. Take an odd number:
2k + 1
and an even number:
2n

Add them together and you get 2k + 2n + 1
This can be written as 2(k + n) + 1 which is an odd number.

Now, to show that an odd number of odd numbers added is odd.

Assume that you have 2n + 1 numbers to add up and each is odd:
Each odd number can be written as an even number + 1. So,

First odd number = 2k(1) + 1 (2 times k sub 2)
2nd odd number = 2k(2) + 1
...
(2n + 1)th = 2k(2n+1) + 1

Add all these numbers together and you get:

2*[k(1) + k(2) + ... +k(2n+1)] + 1 + 1 + ... +1

How many 1's are there? 2n+1 many. So, this equals:
2*[k(1) + k(2) + ... +k(2n+1)] + 2n + 1 =
which is an even number plus an odd and therefore odd.

Answer 3

Odd. For if you write it like this: (2n+1) + (2m+1) + ... + (2L+1) = 2(n + m + ... + L) + (2a+1), where a is the number of odd numbers. And 2(n + m + ... + L) + (2a+1) = 2(n + m + ... + L + a) + 1, so the sum is one more than twice a double, and thus is odd. QED

Answer 4

odd no odd no terms the sum is odd

Answer 5

odd. And an even number of odd numbers would be even.

Answer 6

odd