Question

Rút gọn biểu thức: A = 1 +2+2²+2³+2⁴+...+2¹⁹+2²⁰

 

Answer 1

`A =1 +2 + 2^2 + 2^3 + ... +2^20`

`=> 2A =2 + 2^2 + 2^3 + 2^4 + ....+ 2^21`

`=> 2A -A = (2+ 2^2 + ... + 2^21) - (1 + 2 + 2^2+..+2^20)`

`=> A = 2^21 -1`

Vậy `A = 2^21 -1`

Answer 2

2²¹⁰

Answer 3

2A = 2 + 2² + 2³ + ... + 2²¹

2A - A = 2 + 2² + 2³ + ... + 2²¹ - (1 + 2 + 2³ + ... + 2²⁰)

A = (2 - 2) + (2² - 2²) + ... + (2²⁰ - 2²⁰) -1 + 2²¹

A = 2²¹ - 1

Vậy A = 2²¹ - 1

Answer 4

\(A=1+2+2^2+2^3+2^4+...+2^{19}+2^{20}\)

\(2A=2+2^2+2^3+2^4+2^5+...+2^{20}+2^{21}\)

\(2A-A=\left(2+2^2+2^3+2^4+2^5+...+2^{20}+2^{21}\right)-\left(1+2+2^2+2^3+2^{40}+...+2^{19}+2^{20}\right)\)

\(A=2^{21}-1\)

Answer 5

A = 1 + 2 + 2² + 2³ + 2⁴ + ... + 2¹⁹ + 2²⁰ 

2A = 2. 1 + 2 . 2 + 2² . 2 + 2³. 2 + 2⁴. 2 + ... + 2¹⁹.2 + 2²⁰.2

2A = 2 + 2² + 2³ + 2⁴ + 2⁵ + ... + 2²⁰ + 2²¹

2A - A =(2+2²+ 2³+ 2⁴+ 2⁵+...+ 2²⁰+2²¹ )-(1+2 +2²+ 2³ + 2⁴ + ...+2+2)

1A   = 2²¹ - 1

 A    = 2²¹ - 1

 

 

Answer 6

90