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

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

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

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

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

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

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

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

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

Em cảm ơn ạ.

Ta thấy:
Số hạng thứ nhất:    ¹/₂ = ¹/_1.2
Số hạng thứ hai:    ¹/₆ = ¹/_2.3
Số hạng thứ ba:    ¹/₁₂ = ¹/_3.4
Số hạng thứ tư:    ¹/₂₀ = ¹/_4.5
..................................................
Số hạng thứ một trăm:    ¹/_100.101
Vậy tổng của 100 số hạng đầu của dãy là:
¹/_1.2 + ¹/_2.3 + ¹/_3.4 + ¹/_4.5 + ... + ¹/_100.101
=> 1 - ¹/₂ + ¹/₂ - ¹/₃ + ¹/₃ - ¹/₄ + ¹/₄ - ¹/₅ + ... + ¹/₁₀₀ - ¹/₁₀₁
=> 1 - ¹/₁₀₁
=> ¹⁰⁰/₁₀₁

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

Là sao mik chả hỉu gì cả??????

Ta có : \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}+\frac{1}{110}+\frac{1}{132}\)

= \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}+\frac{1}{10.11}+\frac{1}{11.12}\)

= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}\)

= \(1-\frac{1}{12}=\frac{11}{12}\)

1/2 + 6/ 1 + 12/ 1 + ......... + 1/132 = 1/ 1.2  + 1/2.3  + 1/3.4  + .......... +1/ 11.12  = 1 − 1/2  + 1/'2  − 1/3  + 1/3  − 1/4  + ........... + 1/11  − 1/12  = 1 − 1/12  = 11/12

\(\dfrac{2}{5}+\dfrac{1}{3}=\dfrac{6+5}{15}=\dfrac{11}{15}\)

\(\dfrac{16}{24}+\dfrac{1}{3}=\dfrac{2}{3}+\dfrac{1}{3}=1\)

\(\dfrac{7}{12}+\dfrac{4}{6}+\dfrac{3}{8}=\dfrac{14}{24}+\dfrac{16}{24}+\dfrac{9}{24}=\dfrac{39}{24}=\dfrac{13}{8}\)

\(1+\dfrac{1}{12}=\dfrac{12+1}{12}=\dfrac{13}{12}\)

2/5+1/3= 6/15+5/15=11/15

2/5+1/3=11/15

16/24+1/3=1

7/12+4/6+3/8=13/8

1+1/12=13/12

1/2 + 5/6 + 11/12 + ... + 89/90

= (1 - 1/2) + (1 - 1/6) + (1 - 1/12) + ... + (1 - 1/90)

= (1 - 1/1.2) + (1 - 1/2.3) +(1 - 1/3.4) + ... + (1 - 1/9.10)

= (1 + 1 + 1 + ... + 1) - (1/1.2 + 1/2.3 + 1/3.4 + ... + 1/9.10)

            9 số 1

= 9 - (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/9 - 1/10)

= 9 - (1 - 1/10)

= 9 - 9/10

= 90/10 - 9/10

= 81/10

ta có:

1/6+1/12+1/20+1/30+.........+1/90+1/110

= 1/2x3+1/3x4+1/4x5+1/5x6+....+1/9x10+1/10x11

= 1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+....+1/9-1/10+1/10-1/11

=1/2-1/11=11/22-2/22=9/22

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\)
\(=\left(\frac{1}{2}-\frac{1}{11}\right)+\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{1}{4}-\frac{1}{4}\right)+...+\left(\frac{1}{10}-\frac{1}{10}\right)\)
\(=\frac{1}{2}-\frac{1}{11}=\frac{11}{22}-\frac{2}{22}=\frac{9}{22}\)

Mk bik câu B nè!

2B = 2/3.5 + 2/5.7 + 2/7.9 +.......+2/97.99

2B = 1/3 - 1/5 + 1/5 - 1/7 +.......+ 1/97 - 1/99

2B = 1/3 - 1/99

2B = 32/99

=> B = 16/99 

Bạn có chắc là đúng ko vậy

bài A sai đề rồi bạn coi lại đi

B=1/3.5+1/5.7+1/7.9+...........+1/97.99

B=1.2/2.3.5+1.2/2.5.7+1.2/2.7.9+...+1.2/2.97.99

B=1/2.2/3.5+1/2.2/5.7+1/2.2/7.9+...+1/2.2/97.99

B=1/2(1/3.5+1/5.7+1/7.9+...+1/97.99)

B=1/2(1/3-1/5+1/5-1/7+1/7-1/9+...+1/97-1/99)    (dùng phương pháp khử)

B=1/2(1/3-1/99)

B=1/2.32/99

B=16/99

ơ toán này là toán lớp 5 mà?????