Câu hỏi của Ngọc

Question

Thu gọn phép tính

M=1+ 2 + 2² + 2³ + 2⁴ +... + 2⁹⁹

Mai Trung Hải Phong · Accepted Answer

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

$\Rightarrow2M=2\left(1+2+2^2+2^3+2^4+...+2^{99}\right)$

$\Rightarrow2M=2+2^2+2^3+2^4+2^5+...+2^{100}$

$\Rightarrow2M-M=\left(2+2^2+2^3+2^4+2^5+...+2^{100}\right)-\left(1+2+2^2+2^3+2^4+...+2^{99}\right)$

$\Rightarrow M=2^{100}-1$

Câu trả lời:

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

$\Rightarrow2M=2\left(1+2+2^2+2^3+2^4+...+2^{99}\right)$

$\Rightarrow2M=2+2^2+2^3+2^4+2^5+...+2^{100}$

$\Rightarrow2M-M=\left(2+2^2+2^3+2^4+2^5+...+2^{100}\right)-\left(1+2+2^2+2^3+2^4+...+2^{99}\right)$

$\Rightarrow M=2^{100}-1$