81/10

refer

1/2+5/6+11/12+19/20+29/30+41/42+55/56+71/72+89/90
1-1/2+1-1/6+1-1/12+1-1/20+1-1/30+1-1/42+1-1/56+1-1/72+1-1/90
9 – (1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)
9 –[1/(1x2)+1/(2x3)+1/(3x4)+1/(4x5)+1/(5x6)+1/(6x7)+1/(7x8)+1/(8x9)+1/(9x10)] 
9 – ( 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+1/9-1/10) 
9 – (1 – 1/10) = 9 – 9/10 = 81/10

81/10

=-3/20 nha bạn 
chúc bạn học tốt

A = \(-\dfrac{1}{20}\) + \(\dfrac{-1}{30}\) + \(\dfrac{-1}{42}\) + \(\dfrac{-1}{56}\) + \(\dfrac{-1}{72}\) +  \(\dfrac{-1}{90}\)

A = - ( \(\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\))

A = - ( \(\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}\))

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

A = - (\(\dfrac{1}{4}-\dfrac{1}{10}\))

A = - \(\dfrac{3}{20}\)

D=\(-\dfrac{1}{4.5}\)+(\(-\dfrac{1}{5.6}\))+(\(-\dfrac{1}{6.7}\))+(\(-\dfrac{1}{7.8}\))+(\(-\dfrac{1}{8.9}\))+(\(-\dfrac{1}{9.10}\))

D=\(-\left(\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}\right)\)

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

D=\(-\left(\dfrac{1}{4}-\dfrac{1}{10}\right)\)

D=\(-\dfrac{3}{20}\)

Đặt S=1/6+1/12+1/20+1/30+1/42+1/56+1/72

=>  S=1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+1/8.9

=>  S=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

=>  S=1/2-1/9

=> S=7/18

Vì 7/18<1/2

=> S<1/2

Mọi người k mik nhé, :)))

1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 

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

= 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/8-1/9

= 1/2 - 1/9

= 7/18

Bn tự so sánh vs 1/2 nha

1/6+1/12+1/20+130+1/42+1/56+1/72

=1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9

=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

=1/2-1/9=7/18

ta quy đồng 7/18 và 1/2 bằng 7/18 và 9/18

vậy 1/6+1/12+1/20+1/30+1/42+1/56+1/72 <1/2

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

\(D=\frac{1}{90}-\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{8\cdot9}\right)\)

\(D=\frac{1}{90}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}\right)\)

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

\(D=\frac{1}{90}-\frac{8}{9}=-\frac{79}{90}\)

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

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

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

D=1/90-(1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+1/8.9)

D=1/90-(1/1-1/2+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)

D=1/90-(1/1-1/9)

D=1/90-8/9

D=(-79/90)

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

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

\(D=\frac{1}{90}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\right)\)

\(D=\frac{1}{90}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)\)

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

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

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

\(D=\frac{1}{90}-\frac{90}{80}\)

\(D=\frac{-79}{80}\)

\(\dfrac{1}{3}-\dfrac{1}{12}-\dfrac{1}{20}-\dfrac{1}{30}-\dfrac{1}{42}-\dfrac{1}{56}-\dfrac{1}{72}-\dfrac{1}{90}-\dfrac{1}{110}=x-\dfrac{5}{13}\)

\(\dfrac{1}{3}\) - \(\dfrac{1}{3.4}\) - \(\dfrac{1}{4.5}\) - \(\dfrac{1}{5.6}\) - \(\dfrac{1}{6.7}\) - \(\dfrac{1}{7.8}\)- \(\dfrac{1}{8.9}\) - \(\dfrac{1}{9.10}\) - \(\dfrac{1}{10.11}\) = \(x\) - \(\dfrac{5}{13}\)

\(\dfrac{1}{3}\) - (\(\dfrac{1}{3.4}\) + \(\dfrac{1}{4.5}\) + \(\dfrac{1}{5.6}\) + \(\dfrac{1}{6.7}\)+ \(\dfrac{1}{7.8}\) + \(\dfrac{1}{8.9}\) + \(\dfrac{1}{9.10}\) + \(\dfrac{1}{10.11}\) =\(x\)-\(\dfrac{5}{13}\)

\(\dfrac{1}{3}\)  - (\(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\) +...+ \(\dfrac{1}{9}\) - \(\dfrac{1}{10}\) + \(\dfrac{1}{10}\) - \(\dfrac{1}{11}\)) = \(x\) - \(\dfrac{5}{13}\)

 \(\dfrac{1}{3}\) - (\(\dfrac{1}{3}\) - \(\dfrac{1}{11}\)) =  \(x\) - \(\dfrac{5}{13}\)

\(\dfrac{1}{3}\) - \(\dfrac{1}{3}\) +  \(\dfrac{1}{11}\) =  \(x\) - \(\dfrac{5}{13}\)

         \(x-\dfrac{5}{13}=\dfrac{1}{11}\)

        \(x\)           = \(\dfrac{1}{11}\) + \(\dfrac{5}{13}\)

      \(x\)           = \(\dfrac{68}{143}\)

Em cảm ơn ạ.

a= -8 phần 9

b= 2

a.A=-1/2-1/6-1/12-1/20-1/30-1/42-1/56-1/72=-151/180

Vậy A=151/180

b.B=0,5+0,4+1/3+1/6+5/7-4/35=2

Vậy B=2

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

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\)\(+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{7}-\frac{1}{8}\)\(+\frac{1}{8}-\frac{1}{9}\)

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

\(=\frac{8}{9}\)

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

=1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+1/8.9

=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

=1-1/9

=8/9

\(=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{8.9}\)

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

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

\(=\frac{8}{9}\)

3/20

hok tốt

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

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

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

\(=\frac{1}{4}-\frac{1}{10}=\frac{6}{40}\)