Câu hỏi của Nguyen The Anh

Question

Cho A = 1+2+2²⁺2²+5……… +2⁹⁸⁺2⁹⁹ so sánh A với 5×2⁹⁸

Lê Minh Anh · Accepted Answer

$A=1+2+2^2+2^3+2^4+.....+2^{98}+2^{99}$

$\Rightarrow2A=2+2^2+2^3+2^4+2^5+.....+2^{99}+2^{100}$

$\Rightarrow2A-A=\left(2+2^2+2^3+2^4+.....+2^{99}+2^{100}\right)-\left(1+2+2^2+2^3+.....+2^{98}+2^{99}\right)$

$\Rightarrow A=2^{100}-1=2^{98}\times2^2-1=2^{98}\times4-1< 2^{98}\times5$

Vậy A < 2⁹⁸ x 5

Câu trả lời:

$A=1+2+2^2+2^3+2^4+.....+2^{98}+2^{99}$

$\Rightarrow2A=2+2^2+2^3+2^4+2^5+.....+2^{99}+2^{100}$

$\Rightarrow2A-A=\left(2+2^2+2^3+2^4+.....+2^{99}+2^{100}\right)-\left(1+2+2^2+2^3+.....+2^{98}+2^{99}\right)$

$\Rightarrow A=2^{100}-1=2^{98}\times2^2-1=2^{98}\times4-1< 2^{98}\times5$

Vậy A < 2⁹⁸ x 5