Câu hỏi của Nguyễn Gia Hân

Question

Tính:

1+2+22+23+.........+22008

B=-----------------------------------

1-22009

Lightning Farron · Accepted Answer

Đặt $A=1+2+2^2+...+2^{2008}$

$2A=2\left(1+2+2^2+...+2^{2008}\right)$

$2A=2+2^2+2^3+...+2^{2009}$

$2A-A=\left(2+2^2+...+2^{2009}\right)-\left(1+2+...+2^{2008}\right)$

$A=2^{2009}-1=-\left(1-2^{2009}\right)$

Khi đó $B=\dfrac{A}{1-2^{2009}}=\dfrac{-\left(1-2^{2009}\right)}{1-2^{2009}}=-1$Câu trả lời: Đặt $A=1+2+2^2+...+2^{2008}$

$2A=2\left(1+2+2^2+...+2^{2008}\right)$

$2A=2+2^2+2^3+...+2^{2009}$

$2A-A=\left(2+2^2+...+2^{2009}\right)-\left(1+2+...+2^{2008}\right)$

$A=2^{2009}-1=-\left(1-2^{2009}\right)$

Khi đó $B=\dfrac{A}{1-2^{2009}}=\dfrac{-\left(1-2^{2009}\right)}{1-2^{2009}}=-1$

Đại số lớp 6