Discrete Math Quiz
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PROBLEM-SOLVING & DISCRETE MODELING
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A proof by induction claims that ∑i=1ni2=n(n+1)(2n+1)6\sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6} for all positive integers nn. In the inductive step, a student writes: "Assume the formula holds for kk. Then ∑i=1k+1i2=∑i=1ki2+(k+1)2=k(k+1)(2k+1)6+(k+1)2\sum_{i=1}^{k+1} i^2 = \sum_{i=1}^k i^2 + (k+1)^2 = \frac{k(k+1)(2k+1)}{6} + (k+1)^2." What additional verification is needed to complete the proof?
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