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Apr
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awarded  Popular Question
Sep
21
comment Indirect proof that sum of first n even numbers is $n^2 + n$
Thanks. I get it now. The problem came from a textbook, but the instructor said to solve it by both induction and contraposition. I think the instructor hasn't yet tried to solve it him/herself.
Sep
21
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Sep
21
accepted Indirect proof that sum of first n even numbers is $n^2 + n$
Sep
21
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Sep
21
comment Indirect proof that sum of first n even numbers is $n^2 + n$
I've figured out the correspondence: even numbers are 2*i (i=1..n) and odd numbers are 2*i-1(i=1..n). By assuming that the sum of the first n odd numbers is n^2, I was able to conclude that the sum of the first n even numbers is n^2 + n. But I still don't have a proof that the sum of the first n odd numbers is n^2 (without having to resort to induction, that is). It's not clear from the problem statement that I should accept the odd numbers -> n^2 as fact.
Sep
21
asked Indirect proof that sum of first n even numbers is $n^2 + n$