So sánh: A= 2^0+2^1+2^2+2^3+…+2^2010 B= 2^2010 – 1 Giải dùm em nhó, thank kiu^^ 25/11/2021 Bởi Margaret So sánh: A= 2^0+2^1+2^2+2^3+…+2^2010 B= 2^2010 – 1 Giải dùm em nhó, thank kiu^^
$\begin{array}{l}A = 2^0 + 2^1 + 2^2 + \dots + 2^{2010}\\ \to 2A = 2^1 + 2^2 + 2^3 + \dots +2^{2011}\\ \to 2A – A = (2^1 + 2^2 + 2^3 + \dots +2^{2011}) – (2^0 + 2^1 + 2^2 + \dots +2^{2010})\\ \to A = 2^{2011} – 2^0\\ \to A = 2^{2011} – 1\\ \to A = B\\ Với\,\,B = 2^{2011} – 1 \end{array}$ Bình luận
$\begin{array}{l}A = 2^0 + 2^1 + 2^2 + \dots + 2^{2010}\\ \to 2A = 2^1 + 2^2 + 2^3 + \dots +2^{2011}\\ \to 2A – A = (2^1 + 2^2 + 2^3 + \dots +2^{2011}) – (2^0 + 2^1 + 2^2 + \dots +2^{2010})\\ \to A = 2^{2011} – 2^0\\ \to A = 2^{2011} – 1\\ \to A = B\\ Với\,\,B = 2^{2011} – 1 \end{array}$
A=B