Question

a) Tìm các số nguyên a, b, c, d sao cho |a-b|+|b-c|+|c-d|-|d-a| = 2015

b) Cho A = \(\dfrac{7^{2011}+1}{7^{2013}+1}\) ; B = \(\dfrac{7^{2013}+1}{7^{2015}+1}\) . Hãy so sánh A và B

Answer 1

b, Ta có:

\(14A=\dfrac{7^{2013}+14}{7^{2013}+1}=\dfrac{7^{2013}+1+13}{7^{2013}+1}=\dfrac{7^{2013}+1}{7^{2013}+1}+\dfrac{13}{7^{2013}+1}=1+\dfrac{13}{7^{2013}+1}\)

\(14B=\dfrac{7^{2015}+14}{7^{2015}+1}=\dfrac{7^{2015}+1+13}{7^{2015}+1}=\dfrac{7^{2015}+1}{7^{2015}+1}+\dfrac{13}{7^{2015}+1}=1+\dfrac{13}{7^{2015}+1}\)

\(\)Vì \(7^{2013}+1< 7^{2015}+1\)

\(\dfrac{\Rightarrow13}{7^{2013}+1}>\dfrac{13}{7^{2015}+1}\)

\(\Rightarrow1+\dfrac{13}{7^{2013}+1}>1+\dfrac{13}{7^{2015+1}}\)

\(\Leftrightarrow14A>14B\)

\(\Rightarrow A>B\)