Question

tinh

A=2¹⁰⁰-2⁹⁹-2⁹⁸-...-2²-2-1

Answer 1

A=2^100-2^99-....-2^2-2-1

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

=>2A-A=2^101-2^100-...-2^3-2^2-2-2^100+2^99+...+2^2+2+1

=>2A-A=2^101-2^101+1=1

 vậy A=1

Answer 2

=> A=2¹⁰⁰- (2⁹⁹+2⁹⁸+........+2²+2+1)                (3)

                           B

Ta có: B=2⁹⁹+2⁹⁸+..........+2²+2+1            (1)

=> 2B=2¹⁰⁰+2⁹⁹+..........+2³+2²+2             (2)

Lấy (2) - (1) ta có:  2B-B=(2¹⁰⁰+2⁹⁹+...........+2³+2²+2)-(2⁹⁹+2⁹⁸+.............+2²+2+1)

=> B= 2¹⁰⁰-1

Thay vào (3) ta có: A=2¹⁰⁰- (2¹⁰⁰-1)

=> A=2¹⁰⁰-2¹⁰⁰+1

=> A=1