



 
Vicki, It seems that an induction is not the most transparent reasoning here. \[1 + 3 + 3^2 ...+3^n1 = S\] Multiply by 3: \[3 + 3^2 ....+ 3^n1 + 3^n = 3S\] Subtract the first from the second: \[1 + 0+0+ ... +0 + 3^n = 2S\] Divide by 2 and you have your solution. Using induction is possible, but does not add to the understanding of most students. Walter Whiteley  


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