Question

Só sánh : A= 2^0+2^1+2^2+2^3 + ... + 2^2010 và B = 2^2011

Answer 1

A=\(2^0+2^1+2^2+....+2^{2010}\)

\(2A=2^1+2^2+....+2^{2011}\)

\(2A-A=\left(2^1-2^1\right)+\left(2^2-2^2\right)+....+\left(2^{2010}-2^{2010}\right)+\left(2^{2011}-1\right)\)

\(A=2^{2011}-1\) 

Vì 2²⁰¹¹ - 1 < 2²⁰¹¹

Do đó A < B