5A = 5/3.8 + 5/8.13 + 5/13.18 + ... + 5/33.38 

     = 1/3 - 1/8 + 1/8 - 1/13 + ... + 1/33 - 1/38

     = 1/3 - 1/38 

 5A = 35/114

=> A = 35/114 : 5   = 7/144

7B = 7/3.10 + 7/10.17 + ... + 7/31.38

      = 1/3 - 1/10 + 1/10- 1/17 + .. + 1/31  - 1/38

     = 1/3 - 1/38 

B   =   35/144 :  7 = 5/144

VẬy A> B 

tính tổng đó           

A=1/3.8+1/8.13+1/13.18+...+1/33.38

5A=5/3.8+5/8.13+5/13.18+...+5/33.38

5A=1/3-1/8+1/8-1/13+1/13-1/18+...+1/33-1/38

5A=1/3-1/38

5A=38/114-3/114

5A=35/114

A=35/114:5

A=7/114

B=1/3.10+1/10.17+1/17.24+1/24.31+1/31.38

7B=7/3.10+7/10.17+7/17.24+7/24.31+7/31.38

7B=1/3-1/10+1/0-1/17+1/17-1/24+1/24-1/31+1/31-1/38

7B=1/3-1/38

7B=38/114-3/114

7B=35/114

B=35/114:7

B=5/114

3 câu như nhau cả thôi :v

\(A=\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+...+\frac{1}{55\cdot57}\)

\(A=\frac{1}{2}\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{55\cdot57}\right)\)

\(A=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{55}-\frac{1}{57}\right)\)

\(A=\frac{1}{2}\left(1-\frac{1}{57}\right)\)

\(A=\frac{1}{2}\cdot\frac{56}{57}\)

\(A=\frac{28}{57}\)

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

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

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

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

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

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

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

\(A=\frac{1}{7\cdot12}+\frac{1}{12\cdot17}+\frac{1}{17\cdot22}+...+\frac{1}{52\cdot57}\)

\(A=\frac{1}{5}\left(\frac{5}{7\cdot12}+\frac{5}{12\cdot17}+\frac{5}{17\cdot22}+...+\frac{5}{52\cdot57}\right)\)

\(A=\frac{1}{5}\left(\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+...+\frac{1}{52}-\frac{1}{57}\right)\)

\(A=\frac{1}{5}\left(\frac{1}{7}-\frac{1}{57}\right)=\frac{1}{5}\cdot\frac{50}{399}=\frac{10}{399}\)

\(B=\frac{10}{8\cdot13}+\frac{10}{13\cdot18}+\frac{10}{18\cdot23}+...+\frac{10}{253\cdot258}\)

\(B=\frac{10}{5}\left(\frac{5}{8\cdot13}+\frac{5}{13\cdot18}+\frac{5}{18\cdot23}+...+\frac{5}{253\cdot258}\right)\)

\(B=2\left(\frac{1}{8}-\frac{1}{13}+\frac{1}{13}-\frac{1}{18}+...+\frac{1}{253}-\frac{1}{258}\right)\)

\(B=2\left(\frac{1}{8}-\frac{1}{258}\right)=2\cdot\frac{125}{1032}=\frac{125}{516}\)

*Cái đây giải thích hơi bị " khó hiểu " :

Chỗ mẫu (12 - 7) = (17 - 12) = ... = (57 - 52) = 5

Tử là 1 , mẫu là 5 nên tử/mẫu = 1/5

Hay \(\frac{1}{5}\left(\frac{5}{7\cdot12}+\frac{5}{12\cdot17}+...+\frac{5}{52\cdot57}\right)\)

Còn bạn Trương Bùi Linh thì :

Mẫu = (13 - 8) = (18 - 13) = (23 - 18) = ... = 5

Tử là 10,mẫu là 5 => tử / mẫu = 10/5 = 2