nhóm từng cái vào r` tính ra

Đặt biểu thức cần tính là A, ta có:

A=\(\dfrac{1}{7}\left(\dfrac{7}{3.10}+\dfrac{7}{10.17}+...+\dfrac{7}{73.80}\right)\)

Làm tg tự với những cái khác là ok

Nếu phân số thứ 2 là \(\frac{1}{10.17}\) thì làm như vậy nè

\(\frac{1}{3.10}+\frac{1}{10.17}+...+\frac{1}{73.80}-\frac{1}{2.9}-\frac{1}{9.16}-\frac{1}{16.23}-\frac{1}{23.30}\)

= \(\frac{1}{7}\left(\frac{1}{3}-\frac{1}{10}+\frac{1}{10}-\frac{1}{17}+...+\frac{1}{73}-\frac{1}{80}\right)-\left(\frac{1}{2.9}+\frac{1}{9.16}+\frac{1}{16.23}+\frac{1}{23.30}\right)\)

= \(\frac{1}{7}\left(\frac{1}{3}-\frac{1}{80}\right)-\frac{1}{7}\left(\frac{1}{2}-\frac{1}{9}+\frac{1}{9}-\frac{1}{16}+\frac{1}{16}-\frac{1}{23}+\frac{1}{23}-\frac{1}{30}\right)\)

= \(\frac{1}{7}.\frac{77}{240}-\frac{1}{7}\left(\frac{1}{2}-\frac{1}{30}\right)=\frac{1}{7}.\frac{77}{240}-\frac{1}{7}.\frac{7}{15}\)

= \(\frac{11}{240}-\frac{1}{15}\)

= \(-\frac{1}{48}\)

Hồ Thu Giang nói đúng đấy

1/48

kick nha

Ta có:

P=\(\frac{1}{3.10}\)+\(\frac{1}{10.17}\)+\(\frac{1}{17.24}\)+......+\(\frac{1}{73.80}\)-\(\frac{1}{2.9}\)-\(\frac{1}{9.16}\)-\(\frac{1}{16.23}\)-\(\frac{1}{23.30}\))

P=\(\frac{1}{7}\)\(\times\)(\(\frac{7}{3.10}\)+\(\frac{7}{10.17}\)+\(\frac{7}{17.24}\)+......\(\frac{7}{73.80}\)-\(\frac{7}{2.9}\)-\(\frac{7}{9.16}\)-\(\frac{7}{16.23}\)-\(\frac{7}{23.30}\))

P=\(\frac{1}{7}\)\(\times\)(\(\frac{1}{3}\)-\(\frac{1}{10}\)+\(\frac{1}{10}\)-\(\frac{1}{17}\)+.....+\(\frac{1}{73}\)-\(\frac{1}{80}\)-\(\frac{1}{2}\)-\(\frac{1}{9}\)-......-\(\frac{1}{23}\)-\(\frac{1}{30}\))

P=\(\frac{1}{7}\)\(\times\)(\(\frac{1}{3}\)-\(\frac{1}{80}\))-\(\frac{1}{7}\)(\(\frac{1}{2}\)-\(\frac{1}{30}\))

P=\(\frac{1}{7}\)\(\times\)(\(\frac{1}{3}\)-\(\frac{1}{80}\)-\(\frac{1}{2}\)+\(\frac{1}{30}\))

P=\(\frac{-7}{336}\)

Bài này mk ko tính máy tính nên ko chắc đâu

\(A=\frac{1}{3\cdot10}+\frac{1}{10\cdot17}+\frac{1}{17\cdot24}+...+\frac{1}{73\cdot80}-\frac{1}{2\cdot9}-\frac{1}{9\cdot16}-\frac{1}{16\cdot23}-\frac{1}{23\cdot30}\)

\(A=\frac{1}{7}\left(\frac{7}{3\cdot10}+\frac{7}{10\cdot17}+\frac{7}{17\cdot24}+...+\frac{7}{73\cdot80}-\frac{7}{2\cdot9}-\frac{7}{9\cdot16}-\frac{7}{16\cdot23}-\frac{7}{23\cdot30}\right)\)

\(A=\frac{1}{7}\left(\frac{1}{3}-\frac{1}{10}+\frac{1}{10}-\frac{1}{17}+...+\frac{1}{73}-\frac{1}{80}-\frac{1}{2}+\frac{1}{9}-\frac{1}{9}+\frac{1}{16}-...-\frac{1}{23}-\frac{1}{30}\right)\)

\(A=\frac{1}{7}\left(\frac{1}{3}-\frac{1}{80}-\frac{1}{2}-\frac{1}{30}\right)\)

=1-1/3-1/2+1/4+1/3-1/5-1/4+1/6+...+1/97-1/99-1/98+1/100

=1-1/2-1/99-1/98=2327/4851

\(\dfrac{1}{7}\left(\dfrac{7}{3.10}+\dfrac{7}{10.17}+...+\dfrac{7}{73.80}-\left(\dfrac{7}{2.9}+\dfrac{7}{9.16}+...+\dfrac{7}{23.30}\right)\right)\)

\(=\dfrac{1}{7}\left(\dfrac{1}{3}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{17}+...+\dfrac{1}{73}-\dfrac{1}{80}-\left(\dfrac{1}{2}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{16}+...+\dfrac{1}{23}-\dfrac{1}{30}\right)\right)\)

\(=\dfrac{1}{7}\left(\dfrac{1}{3}-\dfrac{1}{80}-\left(\dfrac{1}{2}-\dfrac{1}{30}\right)\right)\)

\(=\dfrac{1}{7}\left(\dfrac{77}{240}-\dfrac{7}{15}\right)=\dfrac{1}{7}.\left(-\dfrac{7}{48}\right)=-\dfrac{1}{48}\)

dỗiii c-các cậu vì ko lm hộ t-tớ -((

Đặt cái đó=A
Nhân 7A vào rồi áp dụng đến hết 7/n(n+7)=1/n-1/n+7, trùng cái nào thì khử

\(\frac{1}{1.3}-\frac{1}{2.4}+\frac{1}{3.5}-\frac{1}{4.6}+...+\frac{1}{97.99}-\frac{1}{98.100}\)

\(=1-\frac{1}{3}-\frac{1}{2}+\frac{1}{4}+\frac{1}{3}-\frac{1}{5}-\frac{1}{4}+\frac{1}{6}+...+\frac{1}{97}-\frac{1}{99}-\frac{1}{98}+\frac{1}{100}\)

\(=1-\frac{1}{2}-\frac{1}{99}-\frac{1}{98}\)

\(=\frac{2327}{4851}\)

Đặt A=1/1.3 - 1/2.4 +1/3.5 -1/4.6 +.....+1/97.99 -1/98.100

     4A= 4/1.3 -4/2.4 +4/3.5 -4/4.6 +.....+4/97.99 -4/98.100

          =(4/1.3 +4/3.5 +...+4/97.99) - (4/2.4 +4/4.6 +...+4/98.100)

          =(1/1 -1/3+1/3-1/5+...+1/97-1/99)-(1/2 -1/4 -....1/98-1/100)

         =(1/1-1/99)-(1/2-1/100)

         4A=98/99 - 99/100

         A= (98/99-99/100) :4

ngắn gọn nhất nè
1/1.3-1/2.4+1/3.5-1/4.6+...+1/97.99-1/98.100 
= 1- 1/3 - 1/2 + 1/4 + 1/3 - 1/5 - 1/4 + 1/6 + ... + 1/97 - 1/99 - 1/98 + 1/100
= 1 - 1/2 - 1/99 - 1/98
= 2327/4851

1/3.10+1/10.17+......+1/73.80 - 1/2.9 - 1/9.16  -  1/16.23  -  1/23.30

= (7/3.10+7/10.17+......+7/73.80) : 7 - (7/2.9 + 7/9.16  +  7/16.23  +  7/23.30) : 7

= (1/3-1/10+1/10-1/17+...+1/73-1/80) : 7 - (1/2-1/9+1/9-1/16+1/16-1/23+1/23-1/30) : 7

=(1/3-1/80) : 7 - (1/2-1/30) : 7

= 77/240 : 7 - 7/15 : 7

=11/240 - 1/15

= -1/48

Nhấn đúng cho mk nha!!!!!!!!!!!!!