You first launch Algebra Made Easy and select Proof by Induction for Sums in the menu.

Then enter the sigma expression (thats the general formula of the terms to be added) in the top box and the sum-formula in the bottom box as shown below:

In Step1 (the base case) we plug in 1 into both sides of the equation. If we get a matching answer we move on to Step 2.

Now we assume that the given formula is correct for the n-th integer S(n) (really for the first n integers) and add the n+1. term to both sides of the  equation, simplify the right side and get the expected expression for S(n+1)

then proof by induction allowed is to verify the given identity. Voila!!

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