Question

A =1+2+2²+2^{3+ .... +}2²⁰²²

làm nhanh giúp mình

 

Answer 1

\(A=1+2+2^2+...+2^{2022}\)

\(2A=2\cdot\left(1+2+2^2+...+2^{2022}\right)\)

\(2A=2+2^2+2^3+...+2^{2023}\)

\(2A-A=\left(2+2^2+2^3+...+2^{2023}\right)-\left(1+2+2^2+...+2^{2022}\right)\)

\(A=\left(2-2\right)+\left(2^2-2^2\right)+...+\left(2^{2023}-1\right)\)

\(A=0+0+...+2^{2023}-1\)

\(A=2^{2023}-1\)

Vậy: ...