Question

So sánh A và B:

\(A=\frac{7^{2010}+1}{7^{2011}-1}\)

\(B=\frac{7^{2011}+1}{7^{2012}-1}\)

Answer 1

ta có:\(7A=\frac{7\left(7^{2010}+1\right)}{7^{2011}-1}=\frac{7^{2011}+7}{7^{2011}-1}=\frac{7^{2011}-1+8}{7^{2011}-1}=\frac{7^{2011}-1}{7^{2011}-1}+\frac{8}{7^{2011}-1}=1+\frac{8}{7^{2011}-1}\)

\(7B=\frac{7\left(7^{2011}+1\right)}{7^{2012}-1}=\frac{7^{2012}+7}{7^{2012}-1}=\frac{7^{2012}-1+8}{7^{2012}-1}=\frac{7^{2012}-1}{7^{2012}-1}+\frac{8}{7^{2012}-1}=1+\frac{8}{7^{2012}-1}\)

vì 7²⁰¹¹-1<7²⁰¹²-1

\(\Rightarrow\frac{8}{7^{2011}-1}>\frac{8}{7^{2012}-1}\)

=>A>B