Question

Cho A=1+2+2²+...+2⁷⁹+2⁸⁰ va B=2⁸¹.Hay so sanh A va B

Answer 1

A = 1 + 2² + ... + 2⁸⁰

2A = 2 + 2³ + ... + 2⁸¹

2A - A = ( 2 + 2³ + ... + 2⁸¹ ) - ( 1 + 2² + ... + 2⁸⁰ )

A = 2⁸¹ - 1 < 2⁸¹ = B

Vậy A < B

Answer 2

\(A=1+2+2^2+...+2^{79}+2^{80}\)

\(2A=2+2^3+...+2^{80}+2^{81}\)

Do 2A - A = A nên:

\(A=\left(2+2^3+...+2^{80}+2^{81}\right)-\left(1+2+2^2+...+2^{79}+2^{80}\right)\)

\(=2^{81}-1< 2^{81}=B\)

Do đó A < B