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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 ?

It looks like my formula is wrong then, yeah. Don't know how I missed that.

S_N even is infinite set ?

hmm it depend on how the last element looks like see in the even case last number only can be even.

sum of odd \(S_O\)
\(\sum S_O =2n^2+n-(n^2-n)=n^2\)

:O i never knew sum of odds is n^2 weird !!!