Câu hỏi của TOAN 2000

Question

Cho M=1+2^1+2^2+...+2^50 va N=2^51

So sanh M va N

Minh Hiền · Accepted Answer

$M=1+2+2^2+...+2^{50}$

$\Rightarrow2M=2.\left(1+2+2^2+...+2^{50}\right)$

$2M=2+2^2+2^3+...+2^{51}$

$\Rightarrow2M-M=\left(2+2^2+2^3+...+2^{51}\right)-\left(1+2+2^2+...+2^{50}\right)$

$\Rightarrow M=2^{51}-1<2^{51}=N$

Vậy M < N.

Câu trả lời:

$M=1+2+2^2+...+2^{50}$

$\Rightarrow2M=2.\left(1+2+2^2+...+2^{50}\right)$

$2M=2+2^2+2^3+...+2^{51}$

$\Rightarrow2M-M=\left(2+2^2+2^3+...+2^{51}\right)-\left(1+2+2^2+...+2^{50}\right)$

$\Rightarrow M=2^{51}-1<2^{51}=N$

Vậy M < N.