Question

\(1-2+2^2-2^3+...+2^{1000}\)

minh dang can gap ai nhanh minh tick cho

Answer 1

\(A=1-2+2^2-2^3+...+2^{1000}\)

\(2A=2-2^2+2^3-2^4+...+2^{1001}\)

\(2A+A=\left(2-2^2+2^3-2^4+...+2^{1001}\right)+\left(1-2+2^2-2^3+...+2^{1000}\right)\)

\(3A=2^{1001}+1\Leftrightarrow A=\frac{2^{1001}+1}{3}\)