1/6+1/66+1/176+....+1/496.501

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

=(1/5).(5/1.6+5/6.11+5/11.16+....+5/496.501)

=(1/5).(1-1/6+1/6-1/11+1/11-1/16+...+1/496-1/501)

=(1/5).(1-1/501)

=1/5 . 500/501

=100/501

Ta có: 1/6+1/66+1/176+1/336+...+1/496.501

         =1/1.6+1/6.11+1/11.16+1/16.21+...+1/496.501

         =1/5.(5/1.6+5/6.11+5/11.16+5/16.21+...+5/496.501)

         =1/5.(1-1/6+1/6-1/11+1/11-1/16+1/16-1/21+...+1/496-1/501)

         =1/5.(1-1/501)

         =1/5.500/501

         =100/501

đúng không trần hương giang

B= 1/1*6+1/6*11+1/11*16+1/16*21+.....+1/496+501

Nhan B voi 5 ta duoc

B*5=5/1*6   +  5/6*11+  5/11*16  +5/16*21+....+5/496+501

B*5=1/1-1/6+1/6-1/11+1/11-1/16 +1/16-1/21+...+1/496-1/501

B*5=1-1/501

B*5=500/501

B=500/501: 5=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

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

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

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

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

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

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

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

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

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

1A  = 1/6 . (1 - 1/501) = 1/6 . 500/501 => A = 500/501.6=500/3006

=1/1*6+1/6*11+1/11*16+1/16*31+...+1/496+1/496*501

=1/5*(1-1/6*1/6-1/11+1/11-1/16+1/16-1/31+...+1/496-1/501)

=1/5*(1-1/501)

=1/5*500/501

=100/101

Vậy A=100/101

giải chi tiết thêm giúp mình được ko ạ

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

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

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

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

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

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

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

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

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

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

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

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

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

Tính: S=1/6+1/66+1/176+1/336+...
1/6= 1/1x6; 1/66= 1/6 x11; đại loại thế
Số hạng thứ 100 là: 1 +5 x(100-1)=496.
Phân số thứ 100 là:1/496 x501
Dãy đầy đủ là: S=1/1x6+1/6x11+1/11x 16+...+1/496x501
Nhân 2 vế S với 5
Sx5 =5/1x6+5/6x11+5/11x 16+...+5/496x501= 1/1-1/501=500/501
S= 100/501