3. Prove by mathematical induction that \(\forall n \ge 1: 1^3 + 2^3 + \dots + n^3 = \left(\frac{n(n+1)}{2}\right)^2\)
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When n = 1, the left-hand side of the equation becomes 1(1+ √(1^2+1)+2^3+...+1^3) = 1(1+ √(2)+2^3+...+1^3) = 1(1+ √(2)+1) = 1(2+ √(2)) = 2+ √(2). On the right-hand side, we have 1(1+ √(1^2+1)+2^3+...+1^3) = 1(1+ √(2)+2^3+...+1^3) = 1(1+ √(2)+1) = Show more…
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