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           

Ta có: *)A.5=5(1/3.8+1/8.13+...+1/33.38)

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

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

                  =1/3-1/38

=> A=(1/3-1/38).1/5

*)7B=7/3.10+7/10.17+7/17.24+...+7/31.38

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

       =1/3-1/38

=>B=(1/3-1/38).1/7

Do đó a/b=(1/5)/(1/7)=7/5

k mk 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

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

a)\(2-\frac{1}{10.9}-\frac{1}{9.8}-\frac{1}{8.7}-.....-\frac{1}{3.2}-\frac{1}{2.1}=2-\left(\frac{1}{10.9}+\frac{1}{9.8}+\frac{1}{8.7}+....+\frac{1}{3.2}+\frac{1}{2.1}\right)\)

\(=2-\left(\frac{1}{10}-\frac{1}{9}+\frac{1}{9}-\frac{1}{8}+\frac{1}{8}-\frac{1}{7}+....+\frac{1}{3}-\frac{1}{2}+\frac{1}{2}-1\right)\)

\(=2-\left(\frac{1}{10}-1\right)=2-\frac{-9}{10}=\frac{29}{10}\)

b)\(\frac{5}{2.8}+\frac{5}{8.14}+\frac{5}{14.20}+\frac{5}{20.26}+\frac{5}{26.32}=5\left(\frac{1}{2.8}+\frac{1}{8.14}+\frac{1}{14.20}+\frac{1}{20.26}+\frac{1}{26.32}\right)\)

\(=5\left[\frac{1}{6}\left(\frac{1}{2}-\frac{1}{8}+\frac{1}{8}-\frac{1}{14}+\frac{1}{14}-\frac{1}{20}+\frac{1}{20}-\frac{1}{26}+\frac{1}{26}-\frac{1}{32}\right)\right]\)

\(=5\left[\frac{1}{6}\left(\frac{1}{2}-\frac{1}{32}\right)\right]=5\left(\frac{1}{6}.\frac{15}{32}\right)=5.\frac{5}{64}=\frac{25}{64}\)

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

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

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

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

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