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Use Mathematical Induction to Prove That 1+3+9+27+⋯+3n=3n+1−12 for all n≥0. 1 + 3 + 9 + 27 + \cdots + 3 ^ { n } = \frac { 3 ^ { n + 1 } - 1 } { 2 } \text { for all } n \geq 0 \text {. }

Question 22

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Use mathematical induction to prove that 1+3+9+27+⋯+3n=3n+1−12 for all n≥0. 1 + 3 + 9 + 27 + \cdots + 3 ^ { n } = \frac { 3 ^ { n + 1 } - 1 } { 2 } \text { for all } n \geq 0 \text {. }

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