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!

kết quả là 6/91 nhé

= 1/7.8 + 1/8.9 + 1/9.10 + 1/ 10.11 + 1/11.12 + 1/12.13
= 1/7 - 1/8 + 1/8 - 1/9 +......+1/12 - 1/13 
= 1/7 - 1/13 
= 6/91

Đặt tổng trên là A ta có :

 A= 1/ 20 + 1/ 30 + 1/ 42 + 1/ 56 + 1/ 72 + 1/90 + 1/110 + 1 / 123 + 1/ 156

    =  1 / 4 x5 + 1/ 5 x 6 + 1/6x 7 + 1/ 7x8 + 1/8x9 + 1/9x10+ 1/ 10x11+ 1 /11x12 +1/12 x 13

      = 1/4- 1/5 + 1/ 5 - 1/6 + 1/ 6 - 1/7 + 1/ 7 - 1/8 + 1/8 - 1/9 + 1/9 - 1/10+ 1/10 - 1/11 + 1/11 - 1/12+ 1/ 12 - 1/13

       = 1 /4 - 1 /13

        = 9 /52
 

Số cần tìm là:

 A = 1/10 = 0,1

 k nha

A = \(\frac{1}{10}=0,1\)

Tích cho tớ để đủ 250 điểm đi 

\(B=\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}+\dfrac{1}{110}+\dfrac{1}{132}+\dfrac{1}{156}\)

\(B=\dfrac{1}{5\cdot6}+\dfrac{1}{6\cdot7}+\dfrac{1}{7\cdot8}+\dfrac{1}{8\cdot9}+\dfrac{1}{9\cdot10}+\dfrac{1}{10\cdot11}+\dfrac{1}{11\cdot12}+\dfrac{1}{12\cdot13}\)

\(B=\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{13}\)

\(B=\dfrac{1}{5}-\dfrac{1}{13}=\dfrac{8}{65}\)

B=\(\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}+\dfrac{1}{10.11}+\dfrac{1}{11.12}+\dfrac{1}{12.13}\)

B=\(\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-.......-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}\)

B=\(\dfrac{1}{5}-\dfrac{1}{12}=\dfrac{7}{60}\)

(sở dĩ có như trên vì \(\dfrac{1}{x\left(x+1\right)}=\dfrac{1}{x}-\dfrac{1}{x+1}\) nên cứ áp dụng vào là ra  nhé)

B = 1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110 + 1/132 + 1/156

B = 1/5x6 + 1/6x7 + 1/7x8 + 1/8x9 + 1/9x10 + 1/10x11 + 1/11x12 + 1/12x13

B = 1/5 -1/6 + 1/6- 1/7 + 1/7  -1/ 8 + 1/8 -1/9 +1/9 -1/10 + 1/10  - 1/11 + 1/11-1/12 +1/12 -1/13

B = 1/5 - 1/13 

B = 8/65

\(=\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{12.13}\)

áp dụng \(\frac{1}{a.b}=\frac{1}{a}-\frac{1}{b}\)làm sẽ có các số nghịch đảo và được kết quả là 1/4 - 1/13

A = 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110 + 1/132 + 1/156

A = 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9 + 1/9.10 + 1/10.11 + 1/11.12 + 1/12.13

A = 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 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 = 1/4 - 1/13

A = 9/52

1/20 + 1/30 + 1/42 + ... + 1/156

= 1/4.5 + 1/5.6 + 1/6.7 + .... + 1/12.13

= 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + ... + 1/12 - 1/13

= 1/4 - 1/13

= 9/52

\(=\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}\)

\(=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+....+\frac{1}{12}-\frac{1}{13}\)

\(=\frac{1}{4}-\frac{1}{13}=\frac{9}{52}\)

**** 

=1/6*7+1/7*8+1/8*9...+1/14*15

=1/6-1/7+1/7-1/8+...+1/14-1/15

=1/6-1/15

=1/10

1/42 + 1/56 + 1/72 + 1/90 + 1/110 + 1/132 + 1/156 + 1/182 + 1/210

= 1/6.7 + 1/7.8 + 1/8.9 + 1/9.10 + 1/10.11 + 1/11.12 + 1/12.13 + 1/13.14 + 1/14.15

= 1/6 - 1/7 + 1/7 - 1/8 + 1/8 - 1/9 + 1/9 - 1/10 + 1/10 - 1/11 + 1/11 - 1/12 + 1/12 - 1/13 + 1/13 - 1/14 + 1/14 - 1/15

= 1/6 - 1/15

= 1/10