Question

A=1+2+2²+....+2²⁰²⁰+2²⁰²¹

Answer 1

A = 1 + 2 + 2² + ... + 2²⁰²¹
2A = 2 + 4 + 2³ + ... 2²⁰²²
A = 2²⁰²² - 1

Answer 2

\(A=1+2+2^2+...+2^{2020}+2^{2021}\)

\(2A=2+2^2+2^3+...+2^{2021}+2^{2022}\)

\(2A-A=\left(2+2^2+2^3+...+2^{2021}+2^{2022}\right)-\left(1+2+2^2+...+2^{2020}+2^{2021}\right)\)

\(A=2^{2022}-1\)