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by induction step1: prove it's true for n = 1 by direct substitution step2: assume its true for n = k where k is some integer step 3 : evaluate the LHS for n = k+ 1 => this means adding 2(k+1) to LHS step4: also add 2(k+1) to RHS, because you can -- and *must* to keep the equality -- and see if that makes the RHS same as the formula suggests it should be ie (k+1)^2 + (k+1) if so you have proved it. if not, you haven't.
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