\(\dfrac{539}{78}\)

Đáp số là 539/78 nhé

\(\dfrac{539}{78}\)

41/42+55/56+71/72+89/90+109/110+131/132+155/156

=1 - 1/42 + 1 - 1/56 + 1 - 1/72 + 1 - 1/90 + 1 - 1/110 + 1 - 1/132 + 1 - 1/156

=(1+1+1+1+1+1+1)+(1/42 - 1/56 - 1/72 - 1/90 - 1/110 - 1/132 - 1/156)

=7+(1/6x7 - 1/7x8 - 1/8x9 -1/9x10 -1/10x11-1/11x12-1/12x13)

=7+(1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11+1/11-1/12+1/12-1/13)

=7+(1/6-1/13)

=7+(13/78-6/78)

=7+7/78

=546/78+7/78

=553/78

k mình he!!

vì mình làm nhanh nhất !

làm sao để tick vậy bn

11/12+19/20+29/30+41/42+55/56+71/72+89/90+109/110 =

256 phần 33

\(\left(1-\frac{1}{35}\right)\left(1-\frac{1}{36}\right)\left(1-\frac{1}{37}\right)...\left(1-\frac{1}{2010}\right)\left(1-\frac{1}{2011}\right)\)

\(=\frac{34}{35}.\frac{35}{36}.\frac{36}{37}.....\frac{2009}{2010}.\frac{2010}{2011}\)

\(=\frac{34}{2011}\)

\(\frac{41}{42}+\frac{55}{56}+\frac{71}{72}+\frac{89}{90}+\frac{109}{110}+\frac{131}{132}+\frac{155}{156}\)

\(=1-\frac{1}{42}+1-\frac{1}{56}+1-\frac{1}{72}+1-\frac{1}{90}+1-\frac{1}{110}+1-\frac{1}{132}+1-\frac{1}{156}\)

\(=7-\left(\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}+\frac{1}{132}+\frac{1}{156}\right)\)

\(=7-\left(\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}\right)\)

\(=7-\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{12}-\frac{1}{13}\right)\)

\(7-\left(\frac{1}{6}-\frac{1}{13}\right)=6\frac{71}{78}\)

bn đổi thành (1-1/6)+(1-1/12)+.....+(1-1/110)

=9-(1/2.3+1/3.4+...+1/10.11)

đến đây bn tự lằm nha

11/12+19/20+29/30+41/42+55/56+71/72+89/90+109/110

= \(\frac{256}{53}\)

a) \(\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{55}{56}+\frac{71}{72}+\frac{89}{90}\)

\(=1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+1-\frac{1}{30}+1-\frac{1}{42}+1-\frac{1}{56}+1-\frac{1}{72}+1-\frac{1}{90}\)

\(=8-\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\right)\)

\(=8-\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\right)\)

\(=8-\left(\frac{3-2}{2.3}+\frac{4-3}{3.4}+\frac{5-4}{4.5}+\frac{6-5}{5.6}+\frac{7-6}{6.7}+\frac{8-7}{7.8}+\frac{9-8}{8.9}+\frac{10-9}{9.10}\right)\)

\(=8-\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)

\(=8-\left(\frac{1}{2}-\frac{1}{10}\right)=7,6\)

b) Bạn làm tương tự. 

mnbvcxzasdf

976554

1/2+5/6+11/12+19/20+29/30+41/42+55/56+71/72+89/90+109/110= 1 - 1/2 + 1 - 1/6 + 1 - 1/12 .....+1 - 1/110= 10 - ( 1/2 + 1/6 + ...+ 1/110) = 10 - ( 1 - 1/ 2+ 1/2 - 1/ 3+ 1/3 - 1/4 ....+ 1/10 - 1/11)= 10 - (1 - 1/11)= 10 - 10/11 = 100/11 

= 100/11 nha bạn

k cho minh nha

chuc ban hoc tot

= \(\frac{100}{11}\)

k cho mik nha 

thank you