Question

tim x biet

2^x + 2^x+1 + 2^x+2 +...+ 2^x+2020=2^2021-1

Answer 1

2^x+2^x+1+2^x+2+.....+2^x+2020 = 2²⁰²¹ - 1

2^x.(1+2+2²+....+2²⁰²⁰) = 2021 - 1

Đặt M = 1+2+2²+...+2²⁰²⁰

2M = 2+2²+2³+...+2²⁰²¹

2M - M = 2²⁰²¹-1

=> M = 2²⁰²¹ - 1

Thay vào, ta có:

2^x.(2²⁰²¹ - 1) = 2²⁰²¹ - 1

=> 2^x = 1

=> x = 0