Question

Rút gọn

A=2¹⁰⁰-2⁹⁹+2⁹⁸-2^97+.....+2²-2

Answer 1

A=2^100-2^99+2^98-...+2^2-2

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

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

=>3A=2^101-2

=>A=(2^101-2)/3

 

Answer 2

2A = 2¹⁰¹ - 2¹⁰⁰ + 2⁹⁹ - ..... - 2² + 2

2A + A = (-2¹⁰⁰ + 2¹⁰⁰) + .... + (-2² + 2²) +  2¹⁰¹ - 2

3A = 2¹⁰¹ - 2

Vậy A = \(\frac{2^{101}-2}{3}\)

 

Answer 3

A=2^100-2^99+2^98-...+2^2-2

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

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

=>3A=2^101-2

=>a=(2^101-2)/3

Answer 4

A=2¹⁰⁰-2⁹⁹+........+2²-2

2A=2.(2¹⁰⁰-2⁹⁹+.........+2²)

2A=2¹⁰¹-2¹⁰⁰+.....+2²

2A+A=(2¹⁰¹-2¹⁰⁰+.....+2²)+(2¹⁰⁰-2⁹⁹+....+2²+2)

3A=2¹⁰¹+2