Câu hỏi của Phạm Đức Nhân

Question

tìm tổng sau $A=1-2+2^2-2^3+2^4-2^5+...+2^{2014}$

Vương Hải Nam · Accepted Answer

$A=1-2+2^2-2^3+...+2^{2014}$

$\Rightarrow2A=2-2^2+2^3-2^4-...+2^{2015}$

$2A+A=\left(2-2^2+2^3-2^{\text{4}}+...+2^{2015}\right)+\left(1-2+2^2-2^3+...+2^{2014}\right)$

$3A=2^{2015}+1$

$\Rightarrow A=\frac{2^{2015} +1}{3}$

Câu trả lời:

$A=1-2+2^2-2^3+...+2^{2014}$

$\Rightarrow2A=2-2^2+2^3-2^4-...+2^{2015}$

$2A+A=\left(2-2^2+2^3-2^{\text{4}}+...+2^{2015}\right)+\left(1-2+2^2-2^3+...+2^{2014}\right)$

$3A=2^{2015}+1$

$\Rightarrow A=\frac{2^{2015} +1}{3}$