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Year 12 Maths Extension 1 Proof

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Question 1
11864

To prove by mathematical induction that \(1 + 3 + {3^2} + ....... + {3^{n - 1}} = \dfrac{{{3^n} - 1}}{2}\) it is assumed that \(1 + 3 + {3^2} + ....... + {3^{k - 1}} = \dfrac{{{3^k} - 1}}{2}\) and then it is required to show that \(\dfrac{{{3^k} - 1}}{2} + {3^k} = \)

A.

\(\dfrac{{{3^k} - 1}}{2}\)

B.

\(\dfrac{{{3^{k + 1}} - 1}}{2}\)

C.

\(\dfrac{{{3^{k + 1}} + 1}}{2}\)

D.

\(\dfrac{{{3^k} + 1}}{2}\)

\(\dfrac{{{3^{k + 1}} - 1}}{2}\)

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