Câu hỏi của Bảo Bình _ Aquarius

Question

Tìm số tự nhiên n, biết :

2^2n-1 - 2 = 2 + 2² + 2³ + ...... + 2⁹⁹ + 2¹⁰⁰

Kiên-Messi-8A-Boy2k6 · Accepted Answer

ĐặtA = $2+2^2+2^3+...+2^{100}$

$\Rightarrow2A=2^2+2^3+2^4+...+2^{101}$

$\Rightarrow2A-A=\left(2^2+2^3+2^4+...+2^{101}\right)-\left(2+2^2+2^3+...+2^{100}\right)$

$\Rightarrow A=2^{101}-2=2^{2n-1}-2$

$\Rightarrow2^{2n-1}=2^{101}\Rightarrow2n-1=101$

$\Rightarrow n=51$

Câu trả lời:

ĐặtA = $2+2^2+2^3+...+2^{100}$

$\Rightarrow2A=2^2+2^3+2^4+...+2^{101}$

$\Rightarrow2A-A=\left(2^2+2^3+2^4+...+2^{101}\right)-\left(2+2^2+2^3+...+2^{100}\right)$

$\Rightarrow A=2^{101}-2=2^{2n-1}-2$

$\Rightarrow2^{2n-1}=2^{101}\Rightarrow2n-1=101$

$\Rightarrow n=51$

Phong Nguyễn Nam · Answer

Đặt $A=2+2^2+2^3+...+2^{100}$

$2A=2.\left(2+2^2+...+2^{100}\right)$

$2A=2^2+2^3+...+2^{101}$

$2A-A=\left(2^2+2^3+...+2^{101}\right)-\left(2+2^2+...+2^{100}\right)$

$A=2^{101}-2$

Ta có : $2^{2n-1}-2=2^{101}-2$

$\Rightarrow2^{2n-1}=2^{101}$

$\Rightarrow2n-1=101$

$\Rightarrow n=51$

Câu trả lời:

Đặt $A=2+2^2+2^3+...+2^{100}$

$2A=2.\left(2+2^2+...+2^{100}\right)$

$2A=2^2+2^3+...+2^{101}$

$2A-A=\left(2^2+2^3+...+2^{101}\right)-\left(2+2^2+...+2^{100}\right)$

$A=2^{101}-2$

Ta có : $2^{2n-1}-2=2^{101}-2$

$\Rightarrow2^{2n-1}=2^{101}$

$\Rightarrow2n-1=101$

$\Rightarrow n=51$