Tính tổng sau:
52/1.6 + 52/6.11 + 52/26.31
52/1.6 + 52/3.4 +... + 52/26.31
Hình như bạn chép sai đề, mình sửa nhé :
\(S=\dfrac{5^2}{1.6}+\dfrac{5^2}{6.11}+\dfrac{5^2}{11.16}+...+\dfrac{5^2}{26.31}\\ =>\dfrac{S}{5}=\dfrac{5}{1.6}+\dfrac{5}{6.11}+\dfrac{5}{11.16}+...+\dfrac{5}{26.31}\\ =>\dfrac{S}{5}=\dfrac{6-1}{1.6}+\dfrac{11-6}{6.11}+\dfrac{16-11}{11.16}+...+\dfrac{31-26}{26.31}\\ =>\dfrac{S}{5}=1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+...+\dfrac{1}{26}-\dfrac{1}{31}=1-\dfrac{1}{31}=\dfrac{30}{31}\\ =>S=\dfrac{30}{31}.5=\dfrac{150}{31}\)
52/1.6+52/6.11+52/11.16+...+52/101.106
\(=5\left(\dfrac{5}{1\cdot6}+\dfrac{5}{6\cdot11}+...+\dfrac{5}{101\cdot106}\right)\\ =5\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{101}-\dfrac{1}{106}\right)\\ =5\left(1-\dfrac{1}{106}\right)=5\cdot\dfrac{105}{106}=\dfrac{525}{106}\)
Tính giá trị biểu thức:
a) A = -11/23.10/-13 +-11/13.3/-23-2/23
b) B = 1/1.2.3 + 1/2.3.4 + ... + 1/18.19.20
c) C = 52/1.6 + 52/6.11 + 52/11.16 +...+ 52/31.35
d) D = 1. 2 .3 + 2 .4. 6+ 4 .8 .12 + 7 .14 .21/ 1. 3. 5 + 2. 6. 10 + 4 .12 .20 + 7 .21 .35 + 3/5
GIÚP MIK VS AK!
\(B=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+\frac{1}{18\cdot19\cdot20}\)
\(B=\frac{1}{2}\left(\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+\frac{2}{3\cdot4\cdot5}+\frac{2}{18\cdot19\cdot20}\right)\)
\(B=\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+\frac{1}{3\cdot4}-\frac{1}{4\cdot5}+...+\frac{1}{18\cdot19}-\frac{1}{19\cdot20}\right)\)
\(B=\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{19\cdot20}\right)\)
\(B=\frac{1}{2}\cdot\frac{189}{380}=\frac{189}{760}\)
\(C=\frac{52}{1\cdot6}+\frac{52}{6\cdot11}+\frac{52}{11\cdot16}+...+\frac{52}{31\cdot36}\)
\(C=\frac{52}{5}\left(\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+\frac{5}{11\cdot16}+...+\frac{6}{31\cdot36}\right)\)
\(C=\frac{52}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{31}-\frac{1}{36}\right)\)
\(C=\frac{52}{5}\cdot\left(1-\frac{1}{36}\right)\)
\(C=\frac{91}{9}\)
Tính hợp lí tổng sau:
52/ 1.6 + 52/ 6.11 + 52/ 11.6 + 52/ 16.21 + 52/ 21.26 + 52/ 26.31
\(A=\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}+\frac{5^2}{26.31}\)
\(\frac{A}{5}=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+\frac{5}{26.31}\)
\(\frac{A}{5}=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+\frac{1}{26}-\frac{1}{31}\)
\(\frac{A}{5}=1-\frac{1}{31}\)
\(A=\frac{150}{31}\)
Tính các tổng sau một cách hợp lý
1+6+11+16+21+26+31+36+41+46+51
52/1.6+52/6.11+52/11.16+...+52/26.31
_ (1+51)+(6+46)+(11+41)+(16+36)+(21+31)+26
= 52+52+52+52+52+26= 52 x 5+26= 286
_ 5 . ( 5 / 1.6+ 5/ 6.11+ 5/ 11.16+.... + 5/ 26.31)
=5. ( 1/1- 1/6+1/6 -1/11+ 1/11-1/16 +....+1/26-1/31)
= 5. ( 1/1 - 1/31)
= 5. 30/31= 150/31
câu a thì nguyễn thị kim phụng giải đúng rồi còn câu b mình nghĩ cậu ấy làm sai mình sẽ làm lại
b)=5.(5/1.6+5/6.11+5/11.16+5/16.21+5/21.26+5/26.31
=5.(5/1-5/6+5/6-5/11+5/11-5/16+5/16-5/21+5/21-5/26+5/26-5/31)
=5.(5-5/31)
=5.150/31
=750/31
Tính giá trị của biểu thức: \(A=\dfrac{5^2}{1.6}+\dfrac{5^2}{6.11}+...+\dfrac{5^2}{26.31}\)
`A = ( 5^2 )/( 1*6)+(5^2)/(6*11)+.....+(5^2)/(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`
\(A=\dfrac{5^2}{1.6}+\dfrac{5^2}{6.11}+...+\dfrac{5^2}{26.31}\)
\(=5.\left(\dfrac{5}{1.6}+\dfrac{5}{6.11}+...+\dfrac{5}{26.31}\right)\)
\(=5.\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{26}-\dfrac{1}{31}\right)\)
\(=5.\left(1-\dfrac{1}{31}\right)=5.\dfrac{30}{31}=\dfrac{150}{31}\)
Tính nhanh :
Q= 5^2/1.6 +5^2 /6.11 +5^2/11.6 +...+5^2/26.31
\(Q=\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+...+\frac{5^2}{26.31}\)
\(=5\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{26.31}\right)\)
\(=5\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{26}-\frac{1}{31}\right)\)
\(=5\left(1-\frac{1}{31}\right)\)
\(=5\cdot\frac{30}{31}=\frac{150}{31}\)
Bạn nhân 2 lên rồi áp dụng \(\frac{5}{a\times\left(a+5\right)}=\frac{1}{a}-\frac{1}{a+5}\) thì sẽ còn lại là 2Q=1-1/31 =30/31 nên Q=30/62
tính C = 52/1.6 + 52/6.11 + ... + 52 /26.31
\(C=\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{26.31}\)
\(=5\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{26.31}\right)=5\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right)=5.\left(1-\frac{1}{31}\right)=5.\frac{30}{31}=\frac{150}{31}\)
A=5^2/1.6+5^2/6.11+.....+5^2/26.31
\(A=\dfrac{5^2}{1\cdot6}+\dfrac{5^2}{6\cdot11}+...+\dfrac{5^2}{26\cdot31}\)
\(=5\left(\dfrac{5}{1\cdot6}+\dfrac{5}{6\cdot11}+...+\dfrac{5}{26\cdot31}\right)\)
\(=5\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{26}-\dfrac{1}{31}\right)\)
\(=5\left(1-\dfrac{1}{31}\right)=5\cdot\dfrac{30}{31}=\dfrac{150}{31}\)
A=5{5/1.6+5/6.11+.....+5/26.31}
A=5{1-1/6+1/6-1/11+.....+1/26-1/31}
A=5{1-1/31}
A=5.30/31
A=150/31