Question

Giúp mình bài này với: Tính A = 1+2^1+2^2+2^3+...+2^2021

Answer 1

\(2A=2+2^2+2^3+...+2^{2022}\\ 2A-A=\left(2+2^2+2^3+...+2^{2022}\right)-\left(1+2+2^2+...+2^{2021}\right)\\ A=2^{2022}-1\)

Answer 2

A = 1+2¹ + 2² + 2³  +....+ 2²⁰²¹

2A = 2( 1 + 2^1 + 2^2 + 2^3 +....+2^2021)

2A = 2 + 2^2 + 2^3+2^4 +....+ 2^2022

A   = ( 2 + 2^2 + 2^3 + 2^4 + ....+2^2022 ) - ( 1+2^2+2^2+2^3+...+2^2021)

A = ( 2 - 2^1 ) + (2^2 - 2^2) + (2^3-2^3)+....+(2^2021-2^2021) + 2^2022-1

A = 0 + 0 + 0 +....+0 + 2^2022 - 1

A = 2^2022 -1