\(\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+....+\frac{1}{55}\)

=\(\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+....+\frac{2}{110}\)

=\(2.\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+....+\frac{1}{10.11}\right)\)

=\(2.\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+..+\frac{1}{10}-\frac{1}{11}\right)\)

= \(2.\left(\frac{1}{3}-\frac{1}{11}\right)\)

=\(2.\frac{8}{33}\)

= \(\frac{16}{33}\)

\(\frac{9}{11}\)nha kb đi

lấy (1/3 + 1/15 +1/10 + 1/21 ) + (1/36 + 1/28 + 1/6) + (1/45 + 1/55)

      =  (4/50 + 3/70) + 2/100

      = 7/120 + 2/100

      = 9/220

= 9/11

a) \(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}+\frac{1}{195}\)

\(=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}\)

\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\right)\)

\(=\frac{1}{2}.\left(1-\frac{1}{15}\right)\)

\(=\frac{1}{2}.\frac{14}{15}\)

\(=\frac{14}{30}=\frac{7}{15}\)

a)

\(=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}\)

\(=2\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\right)\)

\(=2\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)

\(=2\left(1-\frac{1}{15}\right)\)

\(=2.\frac{14}{15}\)

\(=\frac{28}{15}\)

b)

\(=1+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+\frac{2}{90}+\frac{2}{110}+\frac{2}{132}\)

\(=1+\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+\frac{2}{7.8}+\frac{2}{8.9}+\frac{2}{9.10}+\frac{2}{10.11}+\frac{2}{11.12}\)

                                                                                         \(...\)

câu a mình nhầm phải là ½.(…)

yeah viết được phân số rồi

Vậy à bn

​

nhan ca tu va mau cho 2 sau đó đặt nhân tử chung là 2 ta được
đề = 2(1/20 + 1/30 + 1/42+ 1/56+1/72+1/90+1/110+1/132)

= 2[1/(4.5) +1/(5X6) + 1/(6X7) + 1/(7x8) + 1/(8x9) + 1/(9x10)+ 1/(10x11) + 1/(11x12)]

biến đổi : 1/(4x5) = 1/4 - 1/5....tương tự ta được

= 2[(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)]

mo ngoac rut gon het lại
= 2(1/4 - 1/12) = 1/3

=(5/30+3/30+2/30) : (5/30+3/30-2/30)

=10/30 : 5/30

=10/30 x 30/5

=2

!!! Hok tốt!!!

\(\left(\frac{1}{6}+\frac{1}{10}+\frac{1}{15}\right):\left(\frac{1}{6}+\frac{1}{10}-\frac{1}{15}\right)\)

=\(\frac{10}{30}:\frac{6}{30}\)

\(=\frac{5}{3}\)

\(\left(\frac{1}{6}+\frac{1}{10}+\frac{1}{15}\right):\left(\frac{1}{6}+\frac{1}{10}-\frac{1}{15}\right)\)

\(=\left(\frac{5}{30}+\frac{3}{30}+\frac{2}{30}\right):\left(\frac{5}{30}+\frac{3}{30}-\frac{2}{30}\right)\)

\(=\left(\frac{5+3+2}{30}\right):\left(\frac{5+3-2}{30}\right)\)

\(=\frac{8}{30}:\frac{6}{30}\)

\(=\frac{8}{30}\times\frac{30}{6}\)

\(=\frac{4}{1}\times\frac{1}{3}\)

\(=\frac{4}{3}\)

1 nha bạn

k mik nhé

\(\left(\frac{1}{6}+\frac{1}{10}+\frac{1}{15}\right):\left(\frac{1}{6}+\frac{1}{10}+\frac{1}{15}\right)=1\)

(1/6 + 1/10 + 1/15) : (1/6 +1/10 +1/15)=1 

Chúc bạn học tốt!