Question

[Dương Thị Thảo Nguyên]

Tính

A= 2¹⁰⁰ - 2⁹⁹ - 2⁹⁸ - 2⁹⁷ - .......... - 2² - 2 - 1

Answer 1

[Nguyễn Việt Lâm]

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

Đặt \(B=2^{99}+2^{98}+...+2+1\)

\(\Rightarrow2B=2^{100}+2^{99}+...+2^2+2\)

\(\Rightarrow2B-B=2^{100}-1\Leftrightarrow B=2^{100}-1\)

\(\Rightarrow A=2^{100}-\left(2^{100}-1\right)=1\)