Question

S= 3^0+3^2+3^4+3^6+...+3^2014+3^2016

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Answer 1

\(9S=3^2+3^4+....+3^{2018}\)

\(\Leftrightarrow8S=3^{2018}-1\)

hay \(S=\dfrac{3^{2018}-1}{8}\)

Answer 2

\(S=3^0+3^2+3^4+...+3^{2016}\)

\(\Rightarrow3^2S=3^2+3^4+3^6+...+3^{2016}+3^{2018}\)

\(\Rightarrow9S-S=\left(3^2+3^4+...+3^{2016}+3^{2018}\right)-\left(1+3^2+3^4+...+3^{2016}\right)\)

\(\Rightarrow8S=3^{2018}-1\Rightarrow S=\dfrac{3^{2018}-1}{8}\)