Câu hỏi của Trịnh Thị Minh Kiều

Question

Cho S=1-2+2²-2³+...-2²⁰⁰⁵+2²⁰⁰⁶

a,Tính 2S, 3S

b,Tính 3S-2²⁰⁰⁷

I - Vy Nguyễn · Accepted Answer

a)Ta có: $S=1-2+2^2-2^3+...-2^{2005}+2^{2006}$

$2.S=2-2^2+2^3-2^4+...-2^{2006}+2^{2007}$

$2S+S=\left(2-2^2+2^3-2^4+...-2^{2006}+2^{2007}\right)+\left(1-2+2^2-2^3+...-2^{2005}+2^{2006}\right)$

$3S=2^{2007}+1$

b) $3S-2^{2007}=2^{2007}+1-2^{2007}=1$

Câu trả lời:

a)Ta có: $S=1-2+2^2-2^3+...-2^{2005}+2^{2006}$

$2.S=2-2^2+2^3-2^4+...-2^{2006}+2^{2007}$

$2S+S=\left(2-2^2+2^3-2^4+...-2^{2006}+2^{2007}\right)+\left(1-2+2^2-2^3+...-2^{2005}+2^{2006}\right)$

$3S=2^{2007}+1$

b) $3S-2^{2007}=2^{2007}+1-2^{2007}=1$