SACE Stage 2 Specialist Mathematics Practice Questions - SACE Stage 2 Specialist Mathematics Examination (South Australia) Exam

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In a proof by mathematical induction for the summation formula $\sum_{k=1}^n k = \frac{n(n+1)}{2}$, what is the correct expression for $S_{k+1}$ formed by adding the $(k+1)$-th term to the inductive hypothesis $S_k = \frac{k(k+1)}{2}$?

\frac{k(k+1)}{2} + (k+1) \frac{k(k+1)}{2} + k \frac{k(k+1)}{2} + 1 \frac{k(k+2)}{2}

Correct Answer:

\frac{k(k+1)}{2} + (k+1)

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