Question

so sánh A = 1 + 2^2 + 2^3 + ... + 2^99 + 2^100 và B = 2^101 -1

Answer 1

Ta có \(A=1+2^2+2^3+....+2^{99}+2^{100}\)

\(2A=2+2^3+2^4+2^5+...+2^{100}+2^{101}\)

Suy ra \(2A-A=2^{101}-1=B\)

Do đó A =B

Vậy A =B 

Answer 2

A = 1 + 2^2 + 2^3 + ... + 2^99 + 2^100 

2A = 2 + 2^3 + 2^4 + ... + 2^100 + 2^101 

2A - A = ( 2 + 2^3 + 2^4 + ... + 2^100 + 2^101 ) - ( 1 + 2^2 + 2^3 + ... + 2^99 + 2^100 ) 

A = 2^101 - 1 

Vì A = 2^101 - 1 và B = 2^101 - 1 

=> A = B 

Vậy A=B

Answer 3

A=1+2^2+2^3+...+2^99+2^100

2A=2+2^3+2^4+...+2^100+2^101

2A-A=(2+2^3+2^4+...+2^100+2^101)-(1+2^2+2^3+...+2^99+2^100)

A=2^101-[2-(1+2^2)]

A=2^101-3

Vậy A=2^101-3 và B=2^101-1

=> A<B