I am trying to prove $2+4+6+\cdots +2n=n^2+n$ by mathematical induction. I followed all the steps and the $P_{k+1}$ was $2+4+6+\cdots+2(k+1)=(k+1)^2+k+1$ Starting from the left hand side of the equation I have solved till $k^2+k+2(k+1)$. Now I am stuck here. I don't know how to do it further. Please guide me thanks.
$2+4+6+\cdots+2n=n^2+n$ by mathematical induction
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induction
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3The formulas are wrong, $2^n$ and $2^{k+1}$ should read $2n$ and $2(k+1)$. – 2011-11-06