Bạn ơi, có chắc là 6/280 ở cuối không.

Trả lời nhanh để mink giải câu này cho

lộn \(\frac{6}{208}\) chứ ko phải 6/ 280

\(\frac{6}{1.4}+\frac{6}{4.7}+\frac{6}{7.10}+.....+\frac{6}{13.16}\)

Ta có công thức \(\frac{a}{b.c}=\frac{a}{c-b}.\left(\frac{1}{b}-\frac{1}{c}\right)\)

Dựa vào công thức ta có :

\(\frac{6}{1.4}=\frac{6}{3}.\left(1-\frac{1}{4}\right)\)

\(\frac{6}{4.7}=\frac{6}{3}.\left(\frac{1}{4}-\frac{1}{7}\right)\)

.....................................

\(\frac{6}{13.16}=\frac{6}{3}.\left(\frac{1}{13}-\frac{1}{16}\right)\)

\(\Rightarrow\)\(\frac{6}{4}+\frac{6}{28}+\frac{6}{70}+......+\frac{6}{208}=\frac{6}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+.....+\frac{1}{13}-\frac{1}{16}\right)\)

\(\Rightarrow\)\(\frac{6}{4}+\frac{6}{28}+\frac{6}{70}+.....+\frac{6}{208}=\frac{6}{3}.\left(1-\frac{1}{16}\right)=\frac{6}{3}.\left(\frac{15}{16}\right)=\frac{15}{8}\)

Mink chắc chắn, ai thấy đúng thì ủng hộ mink nha !!!

Ta có: 
               \(\frac{3}{4}+\frac{3}{28}+\frac{3}{70}+\frac{3}{130}+\frac{3}{208}\)
\(=\frac{3}{1\times4}+\frac{3}{4\times7}+\frac{3}{7\times10}+\frac{3}{10\times13}+\frac{3}{13\times16}\)
 \(=\frac{4-1}{1\times4}+\frac{7-4}{4\times7}+\frac{10-7}{7\times10}+\frac{13-10}{10\times13}+\frac{16-13}{13\times16}\)  \(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}\)
 \(=1-\frac{1}{16}\)
 \(=\frac{15}{16}\)
 Chắc chắn đúng nhé !

bn hỏi vào đúng những ngày tết lk  

\(\frac{3}{4}+\frac{3}{28}+\frac{3}{70}+\frac{3}{130}+....+\frac{3}{304}.\)

\(=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+.....+\frac{3}{16.19}\)

\(=\frac{4-1}{1.4}+\frac{7-4}{4.7}+\frac{10-7}{7.10}+\frac{13-10}{10.13}+.....+\frac{19-16}{16.19}\)

\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+....+\frac{1}{16}-\frac{1}{19}\)

\(=1-\frac{1}{19}=\frac{18}{19}\)

3/4+3/28+3/70+3/130+...+3/304

= 3 /1.4 + 3/4.7 + 3/7.10 + 3/10.13 +....+ 3 /16.19

= 1 -1/4 + 1/4 - 1/7 + 1/7 - 1/10 + 1/10 - 1/13 + ...+1/16 - 1/19

= 1 - 1/19

=18/19

3/4+3/28+3/70+3/130+...+3/304

= 3/1.4 + 3/4.7 + 3/7.10 + 3/10.13 + ... + 3/16.19

= 1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/0 + 1/10 - 1/13 + ... + 1/16 - 1/19

= 1 - 1/19

= 18/19

A=\(\frac{3}{4}+\frac{3}{28}+\frac{3}{70}+\frac{3}{130}+\frac{3}{208}+\frac{3}{304}\)

A= \(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}+\frac{3}{16.19}\)

A= \(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+\frac{1}{17}-\frac{1}{19}\)

A= 1 - \(\frac{1}{19}\)

A= \(\frac{18}{19}\)

X=3/4+3/28+...+3/304

X=3/1x4+3/4x7+....+3/13x16

X=1-1/4+1/4-1/7+....+1/13-1/16

X=1-1/16

X=15/16

k cho tớ nha Nguyễn Thu Trang 

A=3/4+3/28+3/70+3/130+3/208+3/304

  =3/1x4+3/4x7+3/7x10+3/10x13+7/13x16+7/16x19

  =3/1-3/4+3/4-3/7+3/7-3/10+3/10-3/13+3/13-3/16+3/16-3/19

  =3/1-3/19=57/19-3/19=54/19

12/13

=3/1.4  + 3/4.7 + 3/7.10 + 3/13.10

=1/1 - 1/4 + 1/4 + 1/7 + 1/7 + 1/10 + 1/10 -  1/13

=8+4/13

=12/13

= \(\dfrac{3}{1.4}+\dfrac{3}{4.7}+\dfrac{3}{7.10}+\dfrac{3}{10.13}\) 

= \(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}=1-\dfrac{1}{13}=\dfrac{12}{13}\)

\(B=\frac{3}{4}+\frac{3}{28}+\frac{3}{70}+\frac{3}{130}+\frac{3}{208}+\frac{3}{304}\)

\(\Rightarrow B=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}+\frac{3}{16.19}\)

\(\Rightarrow B=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}+\frac{1}{16}-\frac{1}{19}\)

\(\Rightarrow B=1-\frac{1}{19}=\frac{18}{19}\)

Vậy \(B=\frac{18}{19}\)

Chúc bn học tốt

B = \(\frac{3}{4}+\frac{3}{28}+\frac{3}{70}+\frac{3}{130}+\frac{3}{208}+\frac{3}{304}\)

= \(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}+\frac{3}{16.19}\)

= \(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-...+\frac{1}{13}-\frac{1}{16}\)

= \(1-\frac{1}{16}\)

= \(\frac{15}{16}\)