(Introductory Real Analysis) - This isn't actually the problem I'm being asked to do, but it's part of it; I'm trying to find the formula for the sum of all even integers, and the way I'm doing it conceptually makes sense to me, but isn't working out mathematically. Why?
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What I'm doing is taking the formulas for both the summation of all positive integers and the summation of all even positive integers and subtracting one from the other, to hopefully yield the summation formula for the sum of all odd positive integers. Why isn't this working?
The formula for the sum of all odd digits is n^2, what am I doing wrong?
How do you know the sum of even numbers is \(n(n+1)\) ?
don't you think it must depend on whether \(n\) is odd or even ?