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4 tháng 7 2018

\(D=\frac{4}{21}+\frac{4}{77}+\frac{4}{165}+\frac{4}{285}+\frac{4}{437}+\frac{4}{621}\)

\(D=\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+\frac{4}{15.19}+\frac{4}{19.23}+\frac{4}{23.27}\)

\(D=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+\frac{1}{15}-\frac{1}{19}+\frac{1}{19}-\frac{1}{23}+\frac{1}{23}-\frac{1}{27}\)

\(D=\frac{1}{3}-\frac{1}{27}\)

\(D=\frac{9}{27}-\frac{1}{27}\)

\(D=\frac{8}{27}\)

4 tháng 7 2018

\(D=\frac{4}{21}+\frac{4}{77}+\frac{4}{165}+\frac{4}{285}+\frac{4}{437}+\frac{4}{621}\)

\(D=\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+\frac{4}{15.19}+\frac{4}{19.23}+\frac{4}{23.27}\)

\(D=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+\frac{1}{15}-\frac{1}{19}+\frac{1}{19}-\frac{1}{23}+\frac{1}{23}-\frac{1}{27}\)

\(D=\frac{1}{3}-\frac{1}{27}\)

\(D=\frac{8}{27}\)

_Chúc bạn học tốt_

Giải:

a)A=1/56+1/72+1/90+1/110+1/132+1/156

   A=1/7.8+1/8.9+1/9.10+1/10.11+1/11.12+1/12.13

   A=1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11+1/11-1/12+1/12-1/13

   A=1/7-1/13

  A=6/91

b)B=4/21+4/77+4/165+4/285+4/437+4/621

   B=4/3.7+4/7.11+4/11.15+4/15.19+4/19.23+4/23.27

   B=1/3-1/7+1/7-1/11+1/11-1/15+1/15-1/19+1/19-1/23+1/23-1/27

   B=1/3-1/27

   B=8/27

c) C=1/21+1/77+1/165+1/285+1/437+1/621

    C=1/3.7+1/7.11+1/11.15+1/15.19+1/19.23+1/23.27

    C=1/4.(4/3.7+4/7.11+4/11.15+4/15.19+4/19.23+4/23.27)

    C=1/4.(1/3-1/7+1/7-1/11+1/11-1/15+1/15-1/19+1/19-1/23+1/23-1/27)

    C=1/4.(1/3-1/27)

    C=1/4.8/27

    C=2/27

d) D=1/1.6+1/6.11+1/11.16+1/16.21+1/21.26+1/26.31

    D=1/5.(5/1.6+5/6.11+5/11.16+5/16.21+5/21.26+5/26.31)

    D=1/5.(1/1-1/6+1/6-1/11+1/11-1/16+1/16-1/21+1/21-1/26+1/26-1/31)

    D=1/5.(1/1-1/31)

    D=1/5.30/31

    D=6/31

Nếu câu d cậu viết thiếu thì làm như vầy nhé!

Chúc bạn học tốt!

Nếu như câu d ko chép sai thì làm thế này nha:

d) D=1/1.6+1/6.11+1/11.16+1/16.21+1/26.31

    D=1/5.(5/1.6+5/6.11+5/11.16+5/16.21)+1/806

    D=1/5.(1/1-1/6+1/6-1/11+1/11-1/16+1/16-1/21)+1/806

    D=1/5.(1/1-1/21)+1/806

    D=1/5.20/21+1/806

    D=4/21+1/806

    D=3245/16926

Chúc bạn học tốt!

23 tháng 7 2021

\(C=\dfrac{1}{21}+\dfrac{1}{77}+\dfrac{1}{165}+\dfrac{1}{285}+\dfrac{1}{437}+\dfrac{1}{621}\) 

\(C=\dfrac{1}{3.7}+\dfrac{1}{7.11}+\dfrac{1}{11.15}+\dfrac{1}{15.19}+\dfrac{1}{19.23}+\dfrac{1}{23.27}\) 

\(C=\dfrac{4}{4}.\left(\dfrac{1}{3.7}+\dfrac{1}{7.11}+\dfrac{1}{11.15}+\dfrac{1}{15.19}+\dfrac{1}{19.23}+\dfrac{1}{23.27}\right)\)  \(C=\dfrac{1}{4}.\left(\dfrac{4}{3.7}+\dfrac{4}{7.11}+\dfrac{4}{11.15}+\dfrac{4}{15.19}+\dfrac{4}{19.23}+\dfrac{4}{23.27}\right)\) \(C=\dfrac{1}{4}.\left(\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{15}+\dfrac{1}{15}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{23}+\dfrac{1}{23}-\dfrac{1}{27}\right)\) \(C=\dfrac{1}{4}.\left(\dfrac{1}{3}-\dfrac{1}{27}\right)\) 

\(C=\dfrac{1}{4}.\left(\dfrac{9}{27}-\dfrac{1}{27}\right)\) 

\(C=\dfrac{1}{4}.\dfrac{8}{27}=\dfrac{2}{27}\)  

Mà \(\dfrac{2}{27}< \dfrac{4}{27}\) hay \(C< \dfrac{4}{27}\) 

\(\Rightarrow C< \dfrac{4}{27}\) ( điều phải chứng tỏ ) 

24 tháng 7 2021

cảm ơn bạn nhiều

9 tháng 6 2017

A = \(\frac{1}{21}+\frac{1}{77}+\frac{1}{165}+\frac{1}{285}+\frac{1}{437}\)

A = \(\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.15}+\frac{1}{15.19}+\frac{1}{19.23}\)

A = \(\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{7}\right)+\frac{1}{4}.\left(\frac{1}{7}-\frac{1}{11}\right)+\frac{1}{4}.\left(\frac{1}{11}-\frac{1}{15}\right)+\frac{1}{4}.\left(\frac{1}{15}-\frac{1}{19}\right)+\frac{1}{4}.\left(\frac{1}{19}-\frac{1}{23}\right)\)

A = \(\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+\frac{1}{15}-\frac{1}{19}+\frac{1}{19}-\frac{1}{23}\right)\)

A = \(\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{23}\right)\)

A = \(\frac{1}{4}.\frac{20}{69}\)

A = \(\frac{5}{69}\)

9 tháng 6 2017

A=\(\frac{5}{69}\)

21 tháng 7 2017

bài trên không sai đâu

12 tháng 4 2018

không sai đâu nhé

24 tháng 7 2016

\(\frac{4}{21}+\frac{4}{77}+\frac{4}{165}+...+\frac{4}{11877}\)

\(=\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{107.111}\)

\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{107}-\frac{1}{111}\)

\(=\frac{1}{3}-\frac{1}{111}\)

\(=\frac{111}{333}-\frac{3}{333}=\frac{108}{333}=\frac{12}{37}\)