Câu hỏi của _Minz_

Question

Tính

A = 2⁰ + 2² + 2⁴ + ... + 2²⁰¹⁴

_Giúp_tui_nhắ

_Tt_t

Nguyễn Việt Hoàng · Accepted Answer

$A=2^0+2^2+2^4+...+2^{2014}$

$\Leftrightarrow4A=2^2+2^4+2^6+...+2^{2016}$

$\Leftrightarrow4A-A=\left(2^2+2^4+2^6+...+2^{2016}\right)-\left(2^0+2^2+2^4+...+2^{2014}\right)$

$\Leftrightarrow3A=2^{2016}-1$

$\Leftrightarrow A=\frac{2^{2016}-1}{3}$

Câu trả lời:

$A=2^0+2^2+2^4+...+2^{2014}$

$\Leftrightarrow4A=2^2+2^4+2^6+...+2^{2016}$

$\Leftrightarrow4A-A=\left(2^2+2^4+2^6+...+2^{2016}\right)-\left(2^0+2^2+2^4+...+2^{2014}\right)$

$\Leftrightarrow3A=2^{2016}-1$

$\Leftrightarrow A=\frac{2^{2016}-1}{3}$