tính nhanh:
\(A=\frac{1}{6}+\frac{1}{66}+\frac{1}{176}+\frac{1}{336}+.....+\frac{1}{496.501}\)
K
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Những câu hỏi liên quan
7 tháng 4 2015
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
PB
12 tháng 3 2018
\(y=\frac{1}{6}+\frac{1}{66}+\frac{1}{176}+...+\frac{1}{496.501}\)
\(\Rightarrow y=\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{496.501}\)
\(\Rightarrow5y=5.(\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{496.501}\)
\(\Rightarrow5y=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{496.501}\)
\(\Rightarrow5y=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{496}-\frac{1}{501}\)
\(\Rightarrow5y=1-\frac{1}{501}\)
\(\Rightarrow5y=\frac{501}{501}-\frac{1}{501}\)
\(\Rightarrow5y=\frac{500}{501}\)
\(\Rightarrow y=\frac{500}{501}\div5\)
\(\Rightarrow y=\frac{500}{501}.\frac{1}{5}\)
\(\Rightarrow y=\frac{100}{501}\)
P
3
13 tháng 6 2019
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
13 tháng 6 2019
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
NH
1
NN
Nguyễn Ngọc Anh Minh
CTVHS
VIP
20 tháng 6 2020
\(5B=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{496.501}\)
\(5B=\frac{6-1}{1.6}+\frac{11-6}{6.11}+\frac{16-11}{11.16}+\frac{21-16}{16.21}+...+\frac{501-496}{496.501}\)
\(5B=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{496}-\frac{1}{501}\)
\(5B=1-\frac{1}{501}=\frac{500}{501}\Rightarrow B=\frac{100}{501}\)
30 tháng 3 2016
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
CN
2
HP
16 tháng 8 2016
\(\frac{1}{6}+\frac{1}{66}+\frac{1}{176}+\frac{1}{336}+...+\frac{1}{1886}\)
\(=\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+\frac{1}{16.21}+...+\frac{1}{41.46}\)
\(=\frac{5}{5}\left(\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+\frac{1}{16.21}+...+\frac{1}{41.46}\right)\)
\(=\frac{1}{5}\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{41.46}\right)\)
\(=\frac{1}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{41}-\frac{1}{46}\right)\)
\(=\frac{1}{5}\left(1-\frac{1}{46}\right)\)
\(=\frac{1}{5}.\frac{45}{46}=\frac{9}{46}\)
16 tháng 8 2016
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
19 tháng 7 2015
\(E=\frac{2}{20}+\frac{2}{30}+...+\frac{2}{240}\)
\(\Rightarrow E=\frac{2}{4.5}+\frac{2}{5.6}+...+\frac{2}{15.16}\)
\(E=2.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\right)\)
\(E=2.\frac{3}{16}=\frac{3}{8}\)
18 tháng 3 2019
\(E=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)
\(E=\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+...+\frac{2}{15.16}\)
\(E=2.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)\)
\(E=2.\left(\frac{1}{4}-\frac{1}{16}\right)\)
\(E=2.\frac{3}{16}\)
\(E=\frac{3}{8}\)
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