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!

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

_Chúc bạn học tốt_

D= 4/21 + 4/77 + 4/165 + 4/285 + 4/437 + 4/621

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

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

D= 1/3 - 1/27

D=9/27 - 1/27

D=8/27

1) $(-81)\cdot27-3^4\cdot(-77)$

$=(-81)\cdot27-81\cdot(-77)$

$=-81\cdot[27+(-77)]$

$=-81\cdot(27-77)$

$=-81\cdot(-50)$

$=81\cdot50$

$=4050$

2) $(-16)\cdot32-(-4)^2\cdot18$

$=(-16)\cdot32-16\cdot18$

$=-16\cdot(32+18)$

$=-16\cdot50$

$=-800$

3) $(-2)^4\cdot289-16\cdot189$

$=16\cdot289+16\cdot(-189)$

$=16\cdot[289+(-189)]$

$=16\cdot(289-189)$

$=16\cdot100$

$=1600$

4) $41\cdot(-18)+41\cdot(-81)-41$

$=1\cdot(-18)+41\cdot(-81)+41\cdot(-1)$

$=41\cdot[(-18)+(-81)+(-1)]$

$=41\cdot(-18-81-1)$

$=41\cdot(-99-1)$

$=41\cdot(-100)$

$=-4100$

5) $17\cdot(-37)-23\cdot37-46\cdot(-37)$

$=17\cdot(-37)+23\cdot(-37)-46\cdot(-37)$

$=-37\cdot(17+23-46)$

$=-37\cdot(40-46)$

$=-37\cdot(-6)$

$=37\cdot6$

$=222$

6) $-48+48\cdot(-78)+48\cdot(-21)$

$=48\cdot(-1)+48\cdot(-78)+48\cdot(-21)$

$=48\cdot[(-1)+(-78)+(-21)]$

$=48\cdot(-1-78-21)$

$=48\cdot(-79-21)$

$=48\cdot(-100)$

$=-4800$

7) $29\cdot(-13)+27\cdot(-29)+(-14)\cdot(-29)$

$=-29\cdot13+27\cdot(-29)+(-14)\cdot(-29)$

$=-29\cdot[13+27+(-14)]$

$=-29\cdot(40-14)$

$=-29\cdot26$

$=-754$

$\text{#}Toru$

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

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

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

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

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

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

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

a, 53 * 39 + 47 * 59 - 53 * 21 - 47 * 21     c, (4³ * 5^{2 -} 4³ ) : ( 4 * 4² ) 

= ( 53 + 47 ) *  39 - ( 53 + 47 ) * 21             = ( 64 * 25 - 64 ) : ( 4 * 16 )

= 100 * 39 - 100 * 21                                    = ( 1600 - 64 ) :  64

= ( 39 - 21 ) * 100                                         = 1536 : 64

= 18 * 100                                                     = 24

= 1800

Tính hợp lí:

a) 53 x 39 + 47 x 39 - 53 x 21 - 47 x 21.

b) 5 x 7 x 77- 7 x 60 + 49 x 25 - 15 x 42

c) ( 43 x 52 - 43 ) : ( 4 x 42 )

d) ( 2 + 5 + 11 +...+ 47 + 65

đ) ( 45 x 16 - 17 ) : ( 28 + 45 x 15 )

Đọc tiếp...

Trả lời:

\(\frac{2}{35}+\frac{4}{77}+\frac{2}{143}+\frac{4}{221}+\frac{6}{391}+\frac{2}{575}+\frac{2}{675}\)

\(=\frac{2}{5.7}+\frac{5}{7.11}+\frac{2}{11.13}+\frac{4}{13.17}+\frac{6}{17.23}+\frac{2}{23.25}+\frac{2}{25.27}\)

\(=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+\frac{1}{17}-\frac{1}{23}+\frac{1}{23}-\frac{1}{25}+\frac{1}{25}-\frac{1}{27}\)

\(=\frac{1}{5}-\frac{1}{27}\)

\(=\frac{22}{135}\)

    3/4×13/21-3/21×7/4+15/4×3/21

= 3/21 x 13/4 - 3/21 x 7/4 + 15/4 x 3/21

= 3/21 x ( 13/4 - 7/4 + 15/4 )

= 3/21 x 21/4

= 3/4

3/4 x 13/21 - 3/21 x 7/4 + 15/4 x 3/21

= 3/21 x 13/4 - 3/21 x 7/4 + 15/4 + 3/21

= 3/21 x ( 13/4 - 7/4 + 15/4 )

= 3/21 x 21/4

= 3/4