Question

 tính tổng 

A=2^0+2^1+....+2^2021

Answer 1

\(A=2^0+2^1+...+2^{2021}\)

\(\Rightarrow2A=2^1+2^2+...+2^{2022}\)

\(\Rightarrow2A-A=2^1+2^2+...+2^{2022}-2^0-2^1-...-2^{2021}=2^{2022}-2^0=2^{2022}-1\)

Answer 2

A = 2⁰ + 2¹ + ... + 2²⁰²¹

2A = 2(2⁰+2¹+...+2²⁰²¹)

2A = 2¹ + 2² + ... + 2²⁰²²

A = ( 2^1 + 2^2 +...+2^2022 ) - ( 2^0 + 2^1 + ...+2^2021 )

A = ( 2^1 - 2^1 ) + ( 2^2 - 2^2 ) + .... + (2^2021 - 2^2021 ) + 2^2022 - 2^0

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

A = 2^2022 - 2^0