Tính:
1, A = 1/1x3 + 1/3x5 + 1/5x7 + ... + 1/2019 x 2021
2, B= 4/11x16 + 4/16x21 + 4/21x26 + ... + 4/61x66
K
Khách
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Những câu hỏi liên quan
NH
4
H9
HT.Phong (9A5)
CTVHS
19 tháng 10 2023
a) \(\dfrac{5}{1\cdot6}+\dfrac{5}{6\cdot11}+...+\dfrac{5}{26\cdot31}\)
\(=1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{26}-\dfrac{1}{31}\)
\(=1-\dfrac{1}{31}\)
\(=\dfrac{30}{31}\)
b) \(\dfrac{4}{11\cdot16}+\dfrac{4}{16\cdot21}+...+\dfrac{4}{61\cdot66}\)
\(=\dfrac{4}{5}\cdot\left(\dfrac{5}{11\cdot16}+\dfrac{5}{16\cdot21}+...+\dfrac{5}{61\cdot66}\right)\)
\(=\dfrac{4}{5}\cdot\left(\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-...+\dfrac{1}{61}-\dfrac{1}{66}\right)\)
\(=\dfrac{4}{5}\cdot\left(\dfrac{1}{11}-\dfrac{1}{66}\right)\)
\(=\dfrac{4}{5}\cdot\dfrac{5}{66}\)
\(=\dfrac{4}{66}\)
\(=\dfrac{2}{33}\)
KV
19 tháng 10 2023
a) A = 5²/(1.6) + 5²/(6.11) + ... + 5²/(26.31)
= 5.[5/(1.6) + 5/(6.11) + ...+ 5/(26.31)]
= 5.(1 - 1/6 + 1/6 - 1/11 + ... + 1/26 - 1/31)
= 5.(1 - 1/31)
= 5.30/31
= 150/31
b) B = 4/(11.16) + 4/(16.21) + ... + 4/(61.66)
= 4/5 .[5/(11.16) + 5/(16.21) + ... + 5/(61.66)]
= 4/5.(1/11 - 1/16 + 1/16 - 1/21 + ... + 1/61 - 1/66)
= 4/5.(1/11 - 1/66)
= 4/5 . 5/66
= 2/33
DN
2
AV
8 tháng 7 2019
E=\(\frac{1}{5}\).(\(\frac{1}{11}-\frac{1}{16}\)+\(\frac{1}{16}-\frac{1}{21}+\frac{1}{21}+\frac{1}{26}+....+\frac{1}{61}-\frac{1}{66}\))
E=\(\frac{1}{5}.\left(\frac{1}{11}-\frac{1}{66}\right)\)=\(\frac{1}{5}.\frac{5}{66}=\frac{1}{66}\)
8 tháng 7 2019
\(E=\frac{1}{11x16}+\frac{1}{16x21}+\frac{1}{21x26}+...+\frac{1}{61x66}\)
\(E=\frac{1}{5}\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}+\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\right)\)
\(E=\frac{1}{5}\left(\frac{1}{11}-\frac{1}{66}\right)\)
\(E=\frac{1}{5}.\frac{5}{66}\)
\(E=\frac{1}{66}\)
NH
1
22 tháng 5 2015
\(C=\frac{1}{11\cdot16}+\frac{1}{16\cdot21}+...+\frac{1}{61\cdot66}=\frac{5}{5}\cdot\left(\frac{1}{11\cdot16}+\frac{1}{16\cdot21}+...+\frac{1}{61\cdot66}\right)\)
\(=\frac{1}{5}\cdot\left(\frac{5}{11\cdot16}+\frac{5}{16\cdot21}+...+\frac{5}{61\cdot66}\right)=\frac{1}{5}\cdot\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\right)\)
\(=\frac{1}{5}\cdot\left[\left(\frac{1}{11}-\frac{1}{66}\right)+\left(\frac{1}{16}-\frac{1}{16}\right)+...+\left(\frac{1}{61}-\frac{1}{61}\right)\right]\)
\(=\frac{1}{5}\cdot\left[\left(\frac{6}{66}-\frac{1}{66}\right)+0+...+0\right]=\frac{1}{5}\cdot\frac{5}{66}=\frac{1\cdot5}{5\cdot66}=\frac{1\cdot1}{1\cdot66}=\frac{1}{66}\)
Vậy \(C=\frac{1}{66}\)
Chúc bạn học tốt!^_^
HQ
1
17 tháng 3 2021
\(A=\frac{10}{11.16}+\frac{10}{16.21}+...+\frac{10}{61.66}\)
\(A=\frac{10}{5}\left(\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\right)\)
\(A=\frac{10}{5}\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\right)\)
\(A=\frac{10}{5}\left(\frac{1}{11}-\frac{1}{66}\right)=\frac{10}{5}.\frac{5}{66}=\frac{5}{33}\)
Vậy A =5/33
21 tháng 11 2018
a) \(A=\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\)
=> \(A=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\)
=> \(A=\frac{1}{11}-\frac{1}{66}=\frac{5}{66}\)
b) \(B=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)
=> \(B=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)
=> \(B=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)
=> \(B=\frac{1}{1}-\frac{1}{7}=\frac{6}{7}\)
21 tháng 11 2018
a, A = 5/11x16 + 5/16x21 + 5/21x26 + ... + 5/61x66
= (5/11 - 5/16) + (5/16 - 5/21) + (5/21 - 5/26) + ... + (5/61 - 5/66)
= 5/11 - 5/66 ( phá ngoặc rồi nhóm biểu thức trên)
= 25/66
b, B = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42
= 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 + 1/6x7
= (1/1 - 1/2) + (1/2-1/3) + (1/3 - 1/4) + (1/4 - 1/5) + ( 1/5 -1/6) + (1/6 - 1/7)
= 1/1 - 1/7 = 6/7
c, C = 7/3x4x5 + 7/4x5x6 + 7/5x6x7 +... + 7/19x20x21
C =7/2 x ( 2/3x4x5 + 2/4x5x6 + ... + 2/19x20x21)
C = 7/2 x [(1/3-1/4-1/5) + (1/4-1/5-1/6) + ...+(1/19-1/20-1/21)]
C = 7/2 x (1/3 - 1/21) (cũng phá ngoặc rồi nhóm như các câu trên)
C = 1
Dễ nhưng dài quá !
10 tháng 9 2019
A = 3/11x16 + 3/16x21 + 3/21x26 +...+3/61x66
A : 3 . 5 = 5/11x16 + 5/16x21 + 5/21x26 +...+5/61x66
A : 3 . 5 = 1/11 - 1/16 + 1/16 - 1/21 + ......+ 1/61 - 1/66
A : 3 . 5 = 1/11 - 1/66
A : 3 . 5 = 5/66
A = 5/66 . 3 : 5
A = 5/22 : 5
A = 1/22
Chúc bạn hoc tốt 
TN
1
26 tháng 5 2018
a) \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{x}=1\)
\(\Rightarrow\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}\right)+\frac{1}{x}=1\)
\(\Rightarrow\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}\right)+\frac{1}{x}=1\)
\(\Rightarrow\frac{1}{2}.\left(1-\frac{1}{9}\right)+\frac{1}{x}=1\)
\(\Rightarrow\frac{1}{2}.\frac{8}{9}+\frac{1}{x}=1\)
\(\Rightarrow\frac{4}{9}+\frac{1}{x}=1\)
\(\Rightarrow\frac{1}{x}=1-\frac{4}{9}\)
\(\Rightarrow\frac{1}{x}=\frac{5}{9}\)
\(\Rightarrow x=\frac{1.9}{5}\)
\(\Rightarrow x=\frac{9}{5}\)
Vậy x = \(\frac{9}{5}\)
b) \(\frac{2}{3}-\frac{1}{3}.\left(x-2\right)=\frac{1}{4}\)
\(\Rightarrow\frac{1}{3}.\left(x-2\right)=\frac{2}{3}-\frac{1}{4}\)
\(\Rightarrow\frac{1}{3}.\left(x-2\right)=\frac{5}{12}\)
\(\Rightarrow x-2=\frac{5}{12}:\frac{1}{3}\)
\(\Rightarrow x-2=\frac{5}{4}\)
\(\Rightarrow x=\frac{5}{4}+2\)
\(\Rightarrow x=\frac{13}{4}\)
Vậy x = \(\frac{13}{4}\)
_Chúc bạn học tốt_
6 tháng 7 2016
\(C=\frac{3}{4}x\frac{8}{9}x\frac{15}{16}x...x\frac{9999}{10000}\)
\(C=\frac{3}{4}x\frac{4x2}{3x3}x\frac{3x5}{2x8}x...x\frac{99x101}{100x100}\)
\(C=...\) ( Tự làm tiếp )
\(E=1\frac{1}{3}x1\frac{1}{8}x1\frac{1}{15}x1\frac{1}{24}x...x1\frac{1}{99}\)
\(E=\frac{4}{3}x\frac{9}{8}x\frac{16}{15}x\frac{25}{24}x...x\frac{100}{99}\)
\(E=....\)( tương tự câu C )
Bài 1:
A = \(\dfrac{1}{1\times3}\) + \(\dfrac{1}{3\times5}\) + \(\dfrac{1}{5\times7}\) +...+ \(\dfrac{1}{2019\times2021}\)
A = \(\dfrac{1}{2}\) \(\times\) ( \(\dfrac{2}{1\times3}\) + \(\dfrac{2}{3\times5}\) + \(\dfrac{2}{5\times7}\)+...+ \(\dfrac{2}{2019\times2021}\))
A = \(\dfrac{1}{2}\) \(\times\)( \(\dfrac{1}{1}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{7}\)+...+ \(\dfrac{1}{2019}\) - \(\dfrac{1}{2021}\))
A = \(\dfrac{1}{2}\) \(\times\) ( \(\dfrac{1}{1}\) - \(\dfrac{1}{2021}\))
A = \(\dfrac{1010}{2021}\)
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