You have a fundamental difficulty here: you cannot prove something that isn't true!.Anyone have any idea how to proceed with this?Show that the sum of an odd number of integers is odd and then deduce that for any positive integer n, if a sum of n odd integers is odd, then n is even.
Halls gave you an example. The sum of any number, odd or even, of even integers is even. Furthermore, the sum of any even number of odd numbers plus any number of even numbers is even. So obviously the sum of three even numbers is even as is the sum of two odd numbers and one even number.The question is what the text says, so I went with that. As for what you stated, can you elaborate on that with some example values? I'm not sure I'm understanding the latter half of the expression and what you're saying.
It is, however, possible to prove that the sum of an odd number of odd integers is odd. But that does not seem to be your problem.
Whoa. We cannot help you prove what you have repeatedly told us is the original proposition because it is false.So by showing both formulas for the odd/even it satisfies both aspects of the original question then?