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

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When proving by induction that the sum of the first $n$ odd positive integers is $\sum_{r=1}^n (2r - 1) = n^2$, which term must be added to $S_k = k^2$ to evaluate $S_{k+1}$?

2k + 1 2k - 1 k + 1 2k + 2

Correct Answer:

2k + 1

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