1. The problem statement, all variables and given/known data I am just learning the joys of mathematical induction, and this problem is giving me fits. 2. Relevant equations I am trying to prove that 2 + 4 + 6 + … + 2n = [2n(n+1)]/2 3. The attempt at a solution The base case is to prove P(1) is correct. Simple enough -- 2 = [2 x 1 (1+1)]/2. The RHS does equal 2, so we are good to go there. Next, substitute k for n. So, now we have 2 + 4 + 6 + … + 2k = [2k(k+1)]/2 We have to replace k with (k + 1), which is what we need to prove in this proof. We can also rewrite the LHS to show 2k + 2(k+1) = [2k(k+1)]/2 -- I suspect this is the step where I have gone off the rails. With a little bit of algebra, I should be able to multiply the equations pout and prove the LHS = RHS, but I am somehow missing something, and I am pretty sure it is in step 3. The example problems I have followed in my text show the algebra is similar problems being pretty straightforward, but I am just not getting how to rewrite the substitution for k with (k + 1) as something mathematically correct. Thank you for your help in advance.