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 Apr4 awarded Autobiographer Apr26 awarded Popular Question Sep21 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. Sep21 awarded Scholar Sep21 awarded Supporter Sep21 accepted Indirect proof that sum of first n even numbers is $n^2 + n$ Sep21 awarded Student Sep21 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. Sep21 asked Indirect proof that sum of first n even numbers is $n^2 + n$