Question

Tính tổng A= 2+2¹+2²+..........+2¹⁰⁰

Answer 1

=>2A=2²+2³+2⁴+...+2¹⁰¹

=>2A-A= ( 2²+2³+2⁴+...+2¹⁰¹)-(2+2²+2³+...+2¹⁰⁰)

=>   A  = 2¹⁰¹-2

Answer 2

Đặt A=2+2^1+2^2+...+2^100

=>2A=2(2+2^1+2^2+...+2^100)

=>2A=2^2+2^2+2^3+....+2^101

=>2A-A=2^2+2^2+2^3+...+2^101-(2+2^1+2^2+...+2^1000

=>A=2^2+2^2+2^3+...+2^101-2-2^1-2^2-...-2^100

=>A=2^2-2^1+(2^2-2^2+2^3-2^3+...+2^100-2^100)+2^101

=>A=2^2-2+2^101

=>A=2+2^101

Vậy A =2+2^101