Câu hỏi của Nguyen Tran Khanh Linh

Question

Cho A=1+2+2²+ 2³+.....+2²⁰⁰⁸; B=2²⁰⁰⁹. chứng tỏ rằng B - A =1

Nguyễn Thị Huyền Thư · Accepted Answer

$2A$$=$$2^2+2^3+2^4+......+2^{2009}$

$2A-A=\left(2+2^2+2^3+2^4+...+2^{2009}\right)-\left(1+2+2^2+2^3+...+2^{2008}\right)$$A=2^{2009}-1$

$B-A=2009-\left(2009-1\right)$

$B-A=1\left(ĐPCM\right)$

Câu trả lời:

$2A$$=$$2^2+2^3+2^4+......+2^{2009}$

$2A-A=\left(2+2^2+2^3+2^4+...+2^{2009}\right)-\left(1+2+2^2+2^3+...+2^{2008}\right)$$A=2^{2009}-1$

$B-A=2009-\left(2009-1\right)$

$B-A=1\left(ĐPCM\right)$