Câu hỏi của Nguyễn Giang

Question

Cho S = 1 - 2 + 2² -2³ +...+2²⁰¹² - 2²⁰¹³ . Tính 3S - 2²⁰¹⁴

Lấp La Lấp Lánh · Accepted Answer

$S=1-2+2^2-2^3+...+2^{2012}-2^{2013}$

$\Rightarrow2S=2-2^2+2^3-2^4+...+2^{2013}-2^{2014}$

$\Rightarrow2S+S=2-2^2+2^3-...-2^{2014}+1-2^2-2^3+...-2^{2013}$

$\Rightarrow3S=1-2^{2014}$$\Rightarrow3S-2^{2014}=1-2^{2015}$

Câu trả lời:

$S=1-2+2^2-2^3+...+2^{2012}-2^{2013}$

$\Rightarrow2S=2-2^2+2^3-2^4+...+2^{2013}-2^{2014}$

$\Rightarrow2S+S=2-2^2+2^3-...-2^{2014}+1-2^2-2^3+...-2^{2013}$

$\Rightarrow3S=1-2^{2014}$$\Rightarrow3S-2^{2014}=1-2^{2015}$