Câu hỏi của Minhchau Trần

Question

Cmr (2+1) (2^2+1) (2^4+1)...(2^1024+1)=1+2+2^2+...+2^2047

Akai Haruma · Accepted Answer

Lời giải:

$ ext{VT}=(2^2-1)(2^2+1)(2^4+1)...(2^{1024}+1)$

$=(2^4-1)(2^4+1)....(2^{1024}+1)$

$=(2^8-1)(2^8+1)....(2^{1024}+1)$

$=(2^{1024})^2-1=2^{2048}-1$

$ ext{VP}=1+2+...+2^{2047}$

$2 ext{VP}=2+2^2+...+2^{2048}$

$\Rightarrow 2 ext{VP}- ext{VP}=2^{2048}-1$

$\Leftrightarrow ext{VP}=2^{2048}-1$

Vậy $ ext{VT}= ext{VP}$

Câu trả lời:

Lời giải:

$ ext{VT}=(2^2-1)(2^2+1)(2^4+1)...(2^{1024}+1)$

$=(2^4-1)(2^4+1)....(2^{1024}+1)$

$=(2^8-1)(2^8+1)....(2^{1024}+1)$

$=(2^{1024})^2-1=2^{2048}-1$

$ ext{VP}=1+2+...+2^{2047}$

$2 ext{VP}=2+2^2+...+2^{2048}$

$\Rightarrow 2 ext{VP}- ext{VP}=2^{2048}-1$

$\Leftrightarrow ext{VP}=2^{2048}-1$

Vậy $ ext{VT}= ext{VP}$

Trên con đường thành công không có... · Answer

undefined

Câu trả lời:

undefined

Lấp La Lấp Lánh · Answer

Đặt $A=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{1024}+1\right)=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{1024}+1\right)=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{1024}+1\right)=2^{2048}-1$

Đặt $B=1+2+2^2+...+2^{2047}$

$\Rightarrow2B=2+2^2+2^3+...+2^{2048}$

$\Rightarrow B=2B-B=2+2^2+2^3+...+2^{2048}-1-2-2^2-...-2^{2047}=2^{2048}-1$

Câu trả lời:

Đặt $A=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{1024}+1\right)=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{1024}+1\right)=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{1024}+1\right)=2^{2048}-1$

Đặt $B=1+2+2^2+...+2^{2047}$

$\Rightarrow2B=2+2^2+2^3+...+2^{2048}$

$\Rightarrow B=2B-B=2+2^2+2^3+...+2^{2048}-1-2-2^2-...-2^{2047}=2^{2048}-1$

Chúng tôi đề xuất

Tài nguyên

Ứng dụng mobile

Bảng xếp hạng

Các khóa học có thể bạn quan tâm

Yêu cầu VIP