1/15+1/21+1/28+...+1/190

=2/30+2/42+2/56+...+2/380

=2/5.6+2/6.7+2/7.8+...+2/19.20

=2.(1/5.6+1/6.7+1/7.8+...+1/19.20)

=2.(1/5-1/6+1/6-1/7+1/7-1/8 +...+1/19-1/20)

=2.(1/5-1/20)

=2.3/20

=6/20=3/10

58/380

nó bằng 59/380

tớ cần cách làm bạn ơi

\(B=2.\left(\frac{1}{30}+\frac{1}{42}+...+\frac{1}{380}\right)\)

\(B=2.\left(\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{19.20}\right)\)

\(B=2.\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{20}\right)\)

\(B=2.\left(\frac{1}{5}-\frac{1}{20}\right)\)

\(B=2.\frac{3}{20}\)

\(B=\frac{3}{10}\)

Đáp án này là chính xác nhất đó, mình thề. k cho mình nhé

b=2/30+2/42+2/56+...+2/380

\(B=\frac{1}{2}.\left(\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+...+\frac{1}{380}\right)\)

\(B=\frac{1}{2}.\left(\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{19.20}\right)\)

\(B=\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{19}-\frac{1}{20}\right)\)

\(B=\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{20}\right)\)

\(B=\frac{1}{2}.\frac{3}{20}\)

\(B=\frac{3}{40}\)

k cho mình nhé

2.S= 1/ 5.6 =1/ 6.7 +1/ 7.8 +...+1/ 19.20

2.S= 1/5-1/20

2S= 3/20

\(A=\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{1}{190}\)

\(A=\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+...+\frac{2}{380}\) ( nhân cả tử và mẫu với 2 )

\(A=\frac{2}{5.6}+\frac{2}{6.7}+\frac{2}{7.8}+...+\frac{2}{19.20}=2\left(\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{19.20}\right)\)

A = \(2\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{20}\right)=2\left(\frac{1}{5}-\frac{1}{20}\right)=2.\frac{3}{20}=\frac{3}{10}\)

B = \(\frac{12}{84}+\frac{12}{210}+\frac{12}{390}+...+\frac{12}{2100}\)

\(B=\frac{4}{28}+\frac{4}{70}+\frac{4}{130}+...+\frac{4}{700}\) ( chia cả tử và mẫu của mỗi phân số cho 3 )

B = \(\frac{4}{4.7}+\frac{4}{7.10}+\frac{4}{10.13}+...+\frac{4}{25.28}=\frac{4}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{25.28}\right)\)

B = \(\frac{4}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{25}-\frac{1}{28}\right)=\frac{4}{3}\left(\frac{1}{4}-\frac{1}{28}\right)=\frac{4}{3}.\frac{6}{28}=\frac{2}{3}\)

B = \(\frac{12}{84}+\frac{12}{210}+\frac{12}{390}+...+\frac{12}{2100}\)

Mik sửa lại đề bài

\(A=2\left(\frac{1}{30}+\frac{1}{42}+.....+\frac{1}{380}\right)=2\left(\frac{6-5}{5.6}+\frac{7-6}{6.7}+.....+\frac{20-19}{20.19}\right)=2\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{20}\right)=2\left(\frac{1}{5}-\frac{1}{20}\right)=\frac{3}{10}\)

\(B=\frac{12}{84}+\frac{12}{210}+.....+\frac{12}{2100}=\frac{4}{28}+\frac{4}{70}+.....+\frac{4}{700}=\frac{4}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+....+\frac{1}{25.28}\right)=\frac{4}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-.....-\frac{1}{28}\right)=\frac{4}{2}.\frac{6}{28}=\frac{3}{7}\)

7/15 nhé bạn!

đặt A=1/6+1/10+1/15+1/21+1/28+1/36+1/45

A*2=(1/6*+1/10+1/15+1/21+1/28+1/36+1/45)*2

A*2=1/12+1/20+1/30+1/42+1/56+1/72+1/90

A*2=1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10

A*2=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-/8+1/8-1/9+1/9-1/10

A*2=1/3-1/10

A*2=7/30

A=7/30 / 2

A=7/15

\(\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}\)

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

\(=2.\left(\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)

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

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

\(=2.\left(\frac{10}{30}-\frac{3}{30}\right)\)

\(=2.\frac{7}{30}\)

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

Chúc bạn học tốt !!! 

\(\frac{4}{5}\)

đặt A=1/6+1/10+1/15+1/21+1/28+1/36+1/45

6A=1+3/5+2/5+2/7+3/14+1/6+2/15

6A=1+1+7/14+1/6+2/15

6A=14/5

A=14/5:6=7/15

\(F=\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{1}{190}\)

\(\Rightarrow F=\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+...+\frac{2}{380}\)

\(\Rightarrow F=\frac{2}{5.6}+\frac{2}{6.7}+\frac{2}{7.8}+...+\frac{2}{19.20}\)

\(\Rightarrow F=2.\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{19}-\frac{1}{20}\right)\)

\(\Rightarrow F=2.\left(\frac{1}{5}-\frac{1}{20}\right)\)

\(\Rightarrow F=2.\frac{3}{20}\)

\(\Rightarrow F=\frac{3}{10}\)