a. $A=-\frac{5}{1.6}-\frac{5}{6.11}-\frac{5}{11.16}-...-\frac{5}{2006.2011}$
$=$$-(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}+...+\frac{1}{2006}-\frac{1}{2011})$
$=-($$1-\frac{1}{2011})=$ $-\frac{2010}{2011}$
b. $M=$$\frac{5^{2018}+1}{5^{2017}+1}=$ $\frac{5(5^{2017}+1)-4}{5^{2017}+1}=$ $5-\frac{4}{5^{2017}+1}$
$N=$$\frac{5^{2017}+1}{5^{2016}+1}=$ $\frac{5(5^{2016}+1)-4}{5^{2016}+1}=$ $5-\frac{4}{5^{2016}+1}$
Ta có: $5^{2017}+1>5^{2016}+1$
⇒ $\frac{4}{5^{2017}+1}<$ $\frac{4}{5^{2016}+1}$
⇒ $5-\frac{4}{5^{2017}+1}>$ $5-\frac{4}{5^{2016}+1}$
⇒ $M>N$