Question

Cho S =\(1\) \(-2+2^2-2^3+.........-2^{2013}+2^{2014}\)

Khi đó \(3S-1=2^n\).Vậỵ n = .....

Answer 1

2S = \(2-2^2+2^3-2^4+...-2^{2014}+2^{2015}\)

2S + S = \(2-2^2+2^3-2^4+...-2^{2014}+2^{2015}+1-2+2^2-2^3+...-2^{2013}+2^{2014}\)

3S = \(2^{2015}+1\)

3S - 1 = \(2^{2015}+1-1=2^{2015}\)

=> n = 2015 

Answer 2

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