em lớp 6  nha

B= 1/2 + 1/6 + 1/12 +1/20 + 1/30 + 1/42 + 1/56 + 1/72

B= 1/1*2 + 1/2*3 + 1/3*4 + 1/4*5 + 1/5*6 + 1/6*7 + 1/7*8 + 1/8*9

B=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9

B=1+0-0-0-0-0-0-0-1/9

B=1-1/9

B=8/9

k em nha

phần A em chịu

còn câu dưới đó e

Sửa đề:

\(\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\)

\(=\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+\dfrac{1}{6\times7}+\dfrac{1}{7\times8}+\dfrac{1}{8\times9}+\dfrac{1}{9\times10}\)

\(=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\)

\(=\dfrac{1}{3}-\dfrac{1}{10}\)

\(=\dfrac{10-3}{30}\)

\(=\dfrac{7}{30}\)

1/12 + 1/20 1/30  + 1/42 + 1/56 + 1/72 + 1/90

= 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9 + 1/9.10

= 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/7 + 1/8 - 1/9 + 1/9 - 1/10

= 1/3 - 1/10

= 7/30

1/12+1/20+1/30+1/42+1/56+1/72+1/90=7/30

\(=\frac{7}{30}\)nhé bạn

A=1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+1/8.9+1/9.10

A=1/2-1/3+1/3-1/4+1/4-1/5+...+1/9-1/10

A=1/2-1/10

A=2/5

1/4

can cach giai ko

\(\text{Ta có: }\)\(\frac{1}{90}-\frac{1}{72}-\frac{1}{56}-\frac{1}{42}-\frac{1}{30}-\frac{1}{20}-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)

\(=\frac{1}{90}-\left(\frac{1}{72}+\frac{1}{56}+\frac{1}{42}+\frac{1}{30}+\frac{1}{20}+\frac{1}{12}+\frac{1}{6}+\frac{1}{2}\right)\)

\(=\frac{1}{90}-\left(\frac{1}{9.8}+\frac{1}{8.7}+\frac{1}{7.6}+\frac{1}{6.5}+\frac{1}{5.4}+\frac{1}{4.3}+\frac{1}{3.2}+\frac{1}{2.1}\right)\)

\(=\frac{1}{90}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{8}-\frac{1}{9}\right)\)

\(=\frac{1}{90}-\left(1-\frac{1}{9}\right)\)

\(=\frac{1}{90}-\frac{8}{9}=-\frac{81}{90}=-\frac{9}{10}\)

<=> 

D = 1/90+1/72+1/56+1/42+1/30+1/20+1/12+1/6+1/2

D = 1/(1x2) + 1/(2x3) + 1/(3x4) + 1/(4x5) + 1/(5x6) + … + 1/(9x10)

D = 1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + …. + 1/9 – 1/10

D = 1 – 1/10

D = 9/10

=1/(9.10)-1/(8.9)-1/(7.8)-1/(6.7)-1/(5.6)-1/(4.5)-1/(3.4)-1/(2.3)-1/(1.2)

sau đó làm tiếp nha bạn

( 1/90 + 1/72 + ... + 1/2)
= - { 1/( 9.10) + 1/(9.8) + ... + 1/( 2.1)}
= - ( 1/9 - 1/10 + 1/8 - 1/9 + ...+ 1 - 1/2) ( 1/90 = 1/(9.10) = 1/9 - 1/10)
= - ( 1 - 1/10)
= -9/10

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\)

\(=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+.....+\frac{1}{9\cdot10}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....+\frac{1}{9}-\frac{1}{10}\)

\(=1-\frac{1}{10}=\frac{9}{10}\)

\(\frac{1}{2}+\frac{1}{6}+.......+\frac{1}{90}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{9.10}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...-\frac{1}{10}\)

=\(1-\frac{1}{10}\)

\(=\frac{9}{10}\)