im trying to solve an inductive proof. The question is for P(n) 2+4+6+8+...+2n = n(n+1)+2. I know to start out you have to first prove the base case is true. then you need to prove the inductive step is true. Therefore i need to prove that n(n+1)+2 + 2(n+1) = (n+1)((n+1)+1)+2 correct? (i dont care if the proof is true or false i just want to know if i have the inductive step equasions set up right)
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Yes, you have the inductive step set up correctly! However, the base case isn't true here since if you let n=1, the left hand side is 2 and the right hand side is 1(2) + 2 = 4. But if you change the right hand side from "n(n+1) + 2" to "n(n+1)" then it will be true.