cho A=\(\frac{38}{11\cdot17}\)+\(\frac{57}{16\cdot16}\)+\(\frac{95}{26\cdot41}\)+\(\frac{76}{41\cdot53}\)
B=\(\frac{21}{11\cdot20}\)+\(\frac{28}{20\cdot32}\)+\(\frac{35}{32\cdot47}\)+\(\frac{14}{47\cdot53}\)
Tính A/B
bài 1 tính nhanh
a) A=\(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{99\cdot101}\)
b) B=\(\frac{3}{1\cdot3}+\frac{3}{3\cdot5}+\frac{3}{57}+...+\frac{3}{49\cdot51}\)
c) C=\(\frac{5^2}{1\cdot6}+\frac{5^2}{6\cdot11}+\frac{5^2}{11\cdot16}+\frac{5^2}{16\cdot21}+\frac{5^2}{21\cdot26}+\frac{5^2}{26\cdot31}\)
d) D=\(\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)
e) E=\(\frac{3}{5\cdot11}+\frac{5}{11\cdot21}+\frac{7}{21\cdot35}+\frac{9}{35\cdot53}\)
f) F=\(\frac{2}{15}+\frac{2}{35}+\frac{2}{99}+\frac{4}{77}\)
giải chi tiết giúp mình nhé thank you very much
A=2/1.3 + 2/3.5 + 2/5.7 + ... + 2/99.101
A= 2 - 1/3 + 1/3 - 1/5 + 1/5 - ... + 2/99 - 2/101
A = 2 - 2/101 = 200/101
B = 3-1/3+1/3-1/5+1/5-...+3/49-3/51
B = 3-3/51(tự tính nhé)
C = 5(5/1.6+5/6.11+5/11.16+....+5/26-5/31
C = 5(5-1/31)(tự tính)
D rút gon cho 2 rồi 3D , sau đó 5(3/.... tương tự các cách làm trên)
2E nhân lên rồi giải giống trên
3F Rồi nhân 4/77 và rút gọn thì tính được
a, A= \(\frac{1}{1}\)- \(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{5}\)+......+\(\frac{1}{99}\)-\(\frac{1}{100}\)
A=\(\frac{1}{1}\)-\(\frac{1}{100}\)+(-\(\frac{1}{3}\)+\(\frac{1}{3}\)-.....-\(\frac{1}{99}\)+\(\frac{1}{99}\))
A=\(\frac{1}{1}\)-\(\frac{1}{100}\)+0
A=1-\(\frac{1}{100}\)=\(\frac{100}{100}\)-\(\frac{1}{100}\)=\(\frac{99}{100}\)
a) A= \(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{99.101}\)
=\(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)
=\(1-\frac{1}{100}=\frac{99}{100}\)
b) \(\frac{3}{1.3}+\frac{3}{3.5}+...+\frac{3}{49.51}\)
=\(\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{49.51}\right).\frac{3}{2}\)
=\(\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{49}-\frac{1}{50}\right).\frac{3}{2}\)
= \(\left(1-\frac{1}{50}\right).\frac{3}{2}=\frac{49}{50}.\frac{3}{2}=\frac{147}{100}\)
c) \(C=\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{26.31}\)
= \(\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{26.31}\right).5\)
= \(\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right).5\)
= \(\left(1-\frac{1}{31}\right).5=\frac{30}{31}.5=\frac{150}{31}\)
Mấy bài còn lại mik đang phải nháp đã. Bạn thông cảm cho mik
a,\(\frac{2}{3}\cdot\left(\frac{1}{3}+\frac{2}{5}\right)\)
b,24+25+26+.....+99+100
c,\(\frac{16\cdot17-5}{16\cdot16+11}\)
d,\(\frac{5}{80}+\frac{5}{90}+\frac{5}{150}+\frac{5}{210}+\frac{5}{270}\)
a) \(\frac{2}{3}.\left(\frac{1}{3}+\frac{2}{5}\right)=\frac{2}{3}.\frac{11}{15}=\frac{22}{45}\)
b) 24+25+26+...+99+100
= (100+24).77:2
= 124.77:2
= 4774
c) \(\frac{16.17-5}{16.16+11}=\frac{16.16+(16-5)}{16.16+11}=\frac{16.16+11}{16.16+11}=1\)
d) \(\frac{5}{80}+\frac{5}{90}+\frac{5}{150}+\frac{5}{210}+\frac{5}{270}\)
\(=\frac{1}{16}+\frac{1}{18}+\frac{1}{30}+\frac{1}{42}+\frac{1}{54}\)
\(=\frac{2929}{15120}\)
a)=\(\frac{2}{3}.\left(\frac{5}{15}+\frac{6}{15}\right)\)
= \(\frac{2}{3}.\frac{11}{15}=\frac{22}{45}\)
d) = 5.(\(\frac{1}{80}+\frac{1}{90}+\frac{1}{150}+\frac{1}{210}+\frac{1}{270}\))
= 50........
kq là tự tính:)))))
Không tính hãy so sánh A và B:
A=\(\frac{16\cdot17-5}{16\cdot16+11}\)
B=\(\frac{45\cdot16-17}{28+45\cdot15}\)
CÁC BẠN GIÚP MK NHA!!!!
A>B em ạ! Vì số âm thì không lớn hơn dương!^.^
\(x-\frac{20}{11\cdot13}-\frac{20}{13\cdot15}-\frac{20}{15\cdot17}-...-\frac{20}{53\cdot55}=\frac{3}{11}\)
\(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{1}{x\left(x+1\right)}=\frac{2}{9}\)
Sửa đề : \(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}\)
\(\Leftrightarrow\)\(\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}\)
\(\Leftrightarrow\)\(2\left(\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2}{9}\)
\(\Leftrightarrow\)\(2\left(\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2}{9}\)
\(\Leftrightarrow\)\(2\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2}{9}\)
\(\Leftrightarrow\)\(2\left(\frac{1}{6}-\frac{1}{x+1}\right)=\frac{2}{9}\)
\(\Leftrightarrow\)\(\frac{1}{6}-\frac{1}{x+1}=\frac{2}{9}.\frac{1}{2}\)
\(\Leftrightarrow\)\(\frac{1}{6}-\frac{1}{x+1}=\frac{1}{9}\)
\(\Leftrightarrow\)\(\frac{1}{x+1}=\frac{1}{6}-\frac{1}{9}\)
\(\Leftrightarrow\)\(\frac{1}{x+1}=\frac{1}{18}\)
\(\Leftrightarrow\)\(x+1=18\)
\(\Leftrightarrow\)\(x=18-1\)
\(\Leftrightarrow\)\(x=17\)
Vậy \(x=17\)
Chúc bạn học tốt ~
\(x-\frac{20}{11.13}-\frac{20}{13.15}-\frac{20}{15.17}-...-\frac{20}{53.55}=\frac{3}{11}\)
\(\Leftrightarrow\)\(x+10\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{53.55}\right)=\frac{3}{11}\)
\(\Leftrightarrow\)\(x+10\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)
\(\Leftrightarrow\)\(x+10\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{11}\)
\(\Leftrightarrow\)\(x+10.\frac{4}{55}=\frac{3}{11}\)
\(\Leftrightarrow\)\(x+\frac{40}{55}=\frac{3}{11}\)
\(\Leftrightarrow\)\(x=\frac{3}{11}-\frac{40}{55}\)
\(\Leftrightarrow\)\(x=\frac{-5}{11}\)
Vậy \(x=\frac{-5}{11}\)
Chúc bạn học tốt ~
\(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{1}{x\left(x+1\right)}=\frac{2}{9}\)
\(\Rightarrow\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+...+\frac{1}{x\left(x+1\right)}=\frac{2}{9}\)
\(\Rightarrow\frac{2}{6\cdot7}+\frac{2}{7\cdot8}+\frac{2}{8\cdot9}+...+\frac{1}{x\left(x+1\right)}=\frac{2}{9}\)
\(\Rightarrow2\left(\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2}{9}\)
\(\Rightarrow2\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2}{9}\)
\(\Rightarrow2\left(\frac{1}{6}-\frac{1}{x+1}\right)=\frac{2}{9}\)
\(\Rightarrow\frac{1}{3}-\frac{2}{x+1}=\frac{2}{9}\)
\(\Rightarrow\frac{2}{x+1}=\frac{1}{9}\)
=> 2.9 = x + 1
=> x + 1 = 18
=> x = 17
Tính nhanh bằng cách hợp lý:
a,\(\frac{14\cdot17-5}{16\cdot16+11}\) c,\(\frac{317\cdot452-201}{451\cdot317+116}\)
b,\(\frac{28+45\cdot15}{45\cdot16-17}\)
(làm đầy đủ nha, làm con nào trước cũng đc miễn là đúng)
a. \(\frac{238-5}{256+11}\) = \(\frac{233}{267}\)
b. \(\frac{28+675}{720-17}\)= \(\frac{703}{703}\) = 1
c. \(\frac{143284-201}{142967+116}\) =\(\frac{143083}{143083}\) =1
ấn đúng cho mik nha
a. \(\frac{7\cdot2\cdot17-5}{8\cdot2\cdot8\cdot2+11}\) = gạch chéo 2 ở trên và 2 ở dưới ( chỉ 2 số 2 bất kì thôi nhé ) , cái này cậu ko cần viết vào mik minh họa thôi cậu phải gạch đấy = \(\frac{119-5}{128+11}\) = \(\frac{114}{139}\)
b.\(\frac{28+5\cdot9\cdot5\cdot3}{5\cdot9\cdot8\cdot2-17}\) = gạch chéo 5 ở trên và 5 ở dưới như ý a ý cũng ko cần viết vào đâu nhớ là chỉ 1 số 5 thôi đấy, gạch thêm số ba và ở dưới thì số 9 đổi thành số 3 = \(\frac{28+9\cdot5}{3\cdot8\cdot2-17}\) = \(\frac{28+45}{48-17}\) = \(\frac{73}{31}\)
c.\(\frac{317\cdot452-201}{451.317+116}\) = gạch chéo số 317 ở trên và dưới như ý a,b =\(\frac{452-201}{451+116}\) = \(\frac{251}{567}\)
Bài 1: Tính
\(\frac{3}{8}.19\frac{1}{3}-\frac{3}{8}.33\frac{1}{3}\)
\(1\frac{4}{23}+\frac{5}{21}-\frac{4}{23}+0,5+\frac{16}{21}\)
\(\frac{21}{47}+\frac{9}{45}+\frac{26}{47}+\frac{4}{5}\)
\(\frac{15}{12}+\frac{5}{13}-\frac{3}{12}-\frac{18}{13}\)
\(\frac{11}{24}-\frac{5}{41}+\frac{13}{24}+0,5-\frac{36}{41}\)
\(\left(-\frac{3}{4}+\frac{2}{3}\right):\frac{5}{11}+\left(-\frac{1}{4}+\frac{1}{3}\right):\frac{5}{11}\)
\(\left(-3\right)^2.\left(\frac{3}{4}-0,25\right)-\left(3\frac{1}{2}-1\frac{1}{2}\right)\)
A = \(\frac{3}{5\cdot11}+\frac{5}{11\cdot21}+\frac{7}{21\cdot35}+\frac{9}{35\cdot53}\) =?
\(\frac{3}{5.11}+\frac{5}{11.21}+\frac{7}{21.35}+\frac{9}{35.53}=\frac{1}{2}\left(\frac{6}{5.11}+\frac{10}{11.21}+\frac{14}{21.35}+\frac{18}{35.53}\right)\)
\(=\frac{1}{2}\left(\frac{1}{5}-\frac{1}{11}+\frac{1}{11}-\frac{1}{21}+\frac{1}{21}-\frac{1}{35}+\frac{1}{35}-\frac{1}{53}\right)=\frac{1}{2}\left(\frac{1}{5}-\frac{1}{53}\right)=\frac{1}{2}.\frac{48}{265}=\frac{24}{265}\)
Sửa lại :
\(=\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{11}+\frac{1}{11}-\frac{1}{21}+\frac{1}{21}-\frac{1}{35}+\frac{1}{35}-\frac{1}{53}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{53}\right)=\frac{1}{2}.\frac{48}{265}=\frac{24}{265}\)
\(2.A=\frac{6}{5.11}+\frac{10}{11.21}+\frac{14}{21.35}+\frac{18}{35.53}\)
\(2.A=\frac{11-5}{5.11}+\frac{21-10}{11.21}+\frac{35-21}{21.35}+\frac{53-35}{35.53}=\frac{1}{5}-\frac{1}{11}+\frac{1}{11}-\frac{1}{21}+\frac{1}{21}-\frac{1}{35}+\frac{1}{35}-\frac{1}{53}\)
\(2A=\frac{1}{5}-\frac{1}{53}=\frac{48}{265}\)
A = \(\frac{48}{265}:2=\frac{24}{265}\)
b3 tính nhanh nếu có thể
a \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
b \(\frac{1}{2}\cdot\frac{1}{2}+\frac{1}{2}\cdot\frac{1}{3}+\frac{1}{3}\cdot\frac{1}{4}+\frac{1}{4}\cdot\frac{1}{5}+\frac{1}{5}\cdot\frac{1}{6}\)
c\(1\frac{1}{24}\cdot5\frac{2}{5}\cdot2-3\frac{7}{9}\cdot2\frac{2}{17}\)
d\(2\frac{3}{13}\cdot\frac{26}{58}\cdot4\cdot2\frac{15}{24}\cdot\frac{8}{21}\)
e \(\left(1-\frac{6}{11}\right)-\frac{5}{11}\)
f\(\left(\frac{15}{7}-\frac{2}{3}\right)+\frac{2}{3}\)
g\(\left(\frac{5}{8}-\frac{1}{4}\right)+\frac{3}{8}\)
\(h\frac{3}{3\cdot5}+\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+\frac{3}{11\cdot14}+\frac{3}{14\cdot17}+\frac{3}{17\cdot20}\)
a) \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+\frac{1}{16}-\frac{1}{32}\)
\(=1-\frac{1}{32}=\frac{31}{32}\)
b) \(\frac{1}{2}.\frac{1}{2}+\frac{1}{2}.\frac{1}{3}+\frac{1}{3}.\frac{1}{4}+\frac{1}{4}.\frac{1}{5}+\frac{1}{5}.\frac{1}{6}\)\
\(=\frac{1}{4}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(\frac{1}{4}-\frac{1}{6}=\frac{1}{12}\)
bài 20 tính bằng phương pháp hợp lí nhất
a \(\frac{31}{23}-\left(\frac{7}{32}+\frac{8}{23}\right)\)
b \(\left(\frac{1}{3}+\frac{12}{67}+\frac{13}{41}\right)-\left(\frac{79}{67}-\frac{28}{41}\right)\)
c\(\frac{38}{45}-\left(\frac{8}{45}-\frac{17}{51}-\frac{3}{11}\right)\)