Ta thay:1/6=1.6; 1/66=6.11; 1/176= 11.16; 1/336= 16.21;...........
=1/6+1/66+1/176+1/376+.....+1/496.501
=1/5.(1-1/501)
=1/5=500/501=100/501
Vay y= 100/501
\(y=\frac{1}{6}+\frac{1}{66}+\frac{1}{176}+...+\frac{1}{496.501}\)
\(\Rightarrow y=\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{496.501}\)
\(\Rightarrow5y=5.(\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{496.501}\)
\(\Rightarrow5y=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{496.501}\)
\(\Rightarrow5y=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{496}-\frac{1}{501}\)
\(\Rightarrow5y=1-\frac{1}{501}\)
\(\Rightarrow5y=\frac{501}{501}-\frac{1}{501}\)
\(\Rightarrow5y=\frac{500}{501}\)
\(\Rightarrow y=\frac{500}{501}\div5\)
\(\Rightarrow y=\frac{500}{501}.\frac{1}{5}\)
\(\Rightarrow y=\frac{100}{501}\)
