Toán Cho A=1+2+2 mũ 2+….+2 mũ 2008 B=2 mũ 2009 17/07/2021 By Aubrey Cho A=1+2+2 mũ 2+….+2 mũ 2008 B=2 mũ 2009
$A=1+2+2^2+…+2^{2008}$ $2A=2+2^2+2^3+…+2^{2009}$ $2A-A=(2+2^2+2^3+…+2^{2009})-(1+2+2^2+…+2^{2008})$ $→A=2^{2009}-1$ Ta thấy: $2^{2009}-1<2^{2009}$ $→A<B$ Vậy $A<B$ Trả lời
A = 1 + 2 + `2^2` + ………….+ `2^2008` 2A = 2 + `2^2` + ………….+ `2^2008` + `2^2009` 2A – A = ( 2 + `2^2` + ………….+ `2^2008` + `2^2009` ) – (1 + 2 + `2^2` + ………….+ `2^2008` ) A = `2^2009` – 1 mà B = `2^2009` > `2^2009` – 1 => B > A XIN HAY NHẤT Ạ Trả lời