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

\(y=\frac{1}{6}+\frac{1}{66}+\frac{1}{176}+...+\frac{1}{496.501}\)

\(\Rightarrow y=\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{496.501}\)

\(\Rightarrow5y=5.(\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{496.501}\)

\(\Rightarrow5y=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{496.501}\)

\(\Rightarrow5y=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{496}-\frac{1}{501}\)

\(\Rightarrow5y=1-\frac{1}{501}\)

\(\Rightarrow5y=\frac{501}{501}-\frac{1}{501}\)

\(\Rightarrow5y=\frac{500}{501}\)

\(\Rightarrow y=\frac{500}{501}\div5\)

\(\Rightarrow y=\frac{500}{501}.\frac{1}{5}\)

\(\Rightarrow y=\frac{100}{501}\)

Quy luật: 
6 = 1.6 
66 = 6.11 
176 = 11.16 
336 = 16.21 
... 
1/(1.6) + 1/(6.11) + 1/(11.16) + … + 1/[(5n-4)(5n+1)] 
=(1/1 – 1/6)/5 + (1/6 – 1/11)/5 + (1/11 – 1/16)/5 +…+ [1/(5n-4) – 1/(5n+1)]/5 
=[1/1 – 1/6 + 1/6 – 1/11 + 1/11 – 1/16 + … + 1/(5n-4) – 1/(5n+1)]/5 
=[1 – 1/(5n+1)]/5 
Tổng 100 số đầu =[1 – 1/(5.100+1)]/5 = 100/501

1/1.6 + 1/6.11+ 1/11.16+ .... 
số thứ 100 có dạng 1/(496.501) 
do đó tổng trên bằng 1/5( 1/1- 1/501) = 100/ 501

hc tốt

\(B=\frac{1}{6}+\frac{1}{66}+\frac{1}{176}+\frac{1}{336}+...+\frac{1}{496.501}\)

\(B=\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+\frac{1}{16.21}+...+\frac{1}{496.501}\)

\(B=\frac{1}{5}.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{496}-\frac{1}{501}\right)\)

\(B=\frac{1}{5}.\left(1-\frac{1}{501}\right)\)

\(B=\frac{1}{5}.\frac{500}{501}=\frac{100}{501}\)

\(5B=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{496.501}\)

\(5B=\frac{6-1}{1.6}+\frac{11-6}{6.11}+\frac{16-11}{11.16}+\frac{21-16}{16.21}+...+\frac{501-496}{496.501}\)

\(5B=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{496}-\frac{1}{501}\)

\(5B=1-\frac{1}{501}=\frac{500}{501}\Rightarrow B=\frac{100}{501}\)

Mới học lớp 5,xin lỗi nha!

B=1/1.6+1/6.11+1/11.16+.....+1/496.501

B=1_1/6+1/6_1/11+1/11_1/16+....+1/496_1/501

B=1_1/501

B=500/501

\(\frac{1}{6}+\frac{1}{66}+\frac{1}{176}+\frac{1}{336}+...+\frac{1}{1886}\)

\(=\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+\frac{1}{16.21}+...+\frac{1}{41.46}\)

\(=\frac{5}{5}\left(\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+\frac{1}{16.21}+...+\frac{1}{41.46}\right)\)

\(=\frac{1}{5}\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{41.46}\right)\)

\(=\frac{1}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{41}-\frac{1}{46}\right)\)

\(=\frac{1}{5}\left(1-\frac{1}{46}\right)\)

\(=\frac{1}{5}.\frac{45}{46}=\frac{9}{46}\)

1/(1.6) + 1/(6.11) + 1/(11.16) + … + 1/[(5n-4)(5n+1)] 
=(1/1 – 1/6)/5 + (1/6 – 1/11)/5 + (1/11 – 1/16)/5 +…+ [1/(5n-4) – 1/(5n+1)]/5 
=[1/1 – 1/6 + 1/6 – 1/11 + 1/11 – 1/16 + … + 1/(5n-4) – 1/(5n+1)]/5 
=[1 – 1/(5n+1)]/5 

=[1 – 1/(5.100+1)]/5 = 100/501

\(E=\frac{2}{20}+\frac{2}{30}+...+\frac{2}{240}\)

\(\Rightarrow E=\frac{2}{4.5}+\frac{2}{5.6}+...+\frac{2}{15.16}\)

\(E=2.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\right)\)

\(E=2.\frac{3}{16}=\frac{3}{8}\)

\(E=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)

\(E=\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+...+\frac{2}{15.16}\)

\(E=2.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)\)

\(E=2.\left(\frac{1}{4}-\frac{1}{16}\right)\)

\(E=2.\frac{3}{16}\)

\(E=\frac{3}{8}\)

\(D=\frac{1}{6}+\frac{1}{66}+\frac{1}{176}+...+\frac{1}{336}\)

\(D=\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{16.21}\)

\(D=\frac{1}{5}.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{16}-\frac{1}{21}\right)\)

\(D=\frac{1}{5}.\left(1-\frac{1}{21}\right)\)

\(D=\frac{1}{5}.\frac{20}{21}\)

\(D=\frac{4}{21}\)