Câu hỏi của Tô Thị Nguyệt Hà

Question

thu gọn

A=$2^1-2^2+2^3-2^4+2^5-2^6+....+2^{2011}-2^{2012}$

Nguyễn Thị Thảo · Accepted Answer

$A=2^1-2^2+...+2^{2011}-2^{2012}$

$\Rightarrow2A=2^2-2^3+...+2^{2012}-2^{2013}$

$\Rightarrow A+2A=\left(2^1-2^2+...+2^{2011}-2^{2012}\right)+\left(2^2-2^3+...+2^{2012}-2^{2013}\right)$

$\Rightarrow3A=2-2^{2013}$

$\Rightarrow A=\dfrac{2-2^{2012}}{3}$Câu trả lời: $A=2^1-2^2+...+2^{2011}-2^{2012}$

$\Rightarrow2A=2^2-2^3+...+2^{2012}-2^{2013}$

$\Rightarrow A+2A=\left(2^1-2^2+...+2^{2011}-2^{2012}\right)+\left(2^2-2^3+...+2^{2012}-2^{2013}\right)$

$\Rightarrow3A=2-2^{2013}$

$\Rightarrow A=\dfrac{2-2^{2012}}{3}$

Ôn tập toán 6