Nhân A với 5 ta được
A .5=5.(1/1.6 +1/6.11+1/11.16+....+1/496.561)
A .5=5/1.6+5/6.11+5/11.16+...+5/496.561
A .5=1-1/6+1/6-1/11+1/11-1/16+...+1/496-1/561
A .5=1-1/561
A .5=560/561
A =560/561 : 5 =112/561
\(\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{496.561}\)
\(=\left(\frac{1}{1}-\frac{1}{6}\right)+\left(\frac{1}{6}-\frac{1}{11}\right)+\left(\frac{1}{11}-\frac{1}{16}\right)+...+\left(\frac{1}{496}-\frac{1}{561}\right)\)
\(=\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{496}-\frac{1}{561}\)
\(=\frac{1}{1}-\frac{1}{561}\)
\(=\frac{561}{561}-\frac{1}{561}\)
\(=\frac{560}{561}\)
\(\Rightarrow\) Vậy, \(A=\frac{560}{561}\)
=1-1/6+1/6-1/11+1/11-1/16+...+1/496-1/561
=1-1/561
=560/561
