ahartley6399 ahartley6399

24-08-2016
Mathematics

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What is the sum of the first eight terms of the geometric series 2 + 6 + 18 + 54 + … ?

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24-08-2016

Hello,
\(u_{1} =2\\ u_{2} =2*3\\ u_{3} =2*3^2\\ ... u_{8} =2*3^7\\ \sum_{i=0}^7\ 2*3^i\\ =2(1+3+3^2+...+3^7)\\ =2* \dfrac{3^8-1}{3-1}\\ =2* \dfrac{6560}{2} \\ =6560\)

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