\(B=\dfrac{5}{11.16}+\dfrac{5}{16.21}+...+\dfrac{5}{61.66}\)Tính giá trị biểu thức:
\(B=\dfrac{5}{11.16}+\dfrac{5}{16.21}+...+\dfrac{5}{61.66}\)
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DV
1
ND
Nguyễn Đăng Nhân
CTVHS
20 tháng 9 2023
Đặt:
\(A=\dfrac{7}{11\cdot16}+\dfrac{7}{16\cdot21}+\dfrac{7}{21\cdot26}+...+\dfrac{7}{61\cdot66}\)
\(\dfrac{5}{7}A=\dfrac{5}{11\cdot16}+\dfrac{5}{16\cdot21}+...+\dfrac{5}{61\cdot66}\)
\(\dfrac{5}{7}A=\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+...+\dfrac{1}{61}-\dfrac{1}{66}\)
\(\dfrac{5}{7}A=\dfrac{1}{11}-\dfrac{1}{66}=\dfrac{6}{66}-\dfrac{1}{66}=\dfrac{5}{66}\)
\(A=\dfrac{5}{66}\cdot\dfrac{7}{5}=\dfrac{7}{66}\)
2 tháng 5 2021
Giải:
a) S=52/1.6+52/6.11+52/11.16+52/16.21+52/21.26
S=5.(5.1/6+5/6.11+5/11.16+5/16.21+5/21.26)
S=5.(1/1-1/6+1/6-1/11+1/11-1/16+1/16-1/21+1/21-1/26)
S=5.(1/1-1/26)
S=5.25/26
S=125/26
b) (1-1/2).(1-1/3).(1-1/4).(1-1/5).....(1-1/19).(1-1/20)
=1/2.2/3.3/4.4/5.....18/19.19/20
=1.2.3.4.....18.19/2.3.4.5.....19.20
=1/20
Chúc bạn học tốt!
18 tháng 10 2015
\(=>A=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\)
\(=>A=\frac{1}{11}-\frac{1}{66}\)
\(=>A=\frac{5}{66}\)
li ke nha
18 tháng 10 2015
A= 5/11.16 + 5/16.21 + .....+5/61.66
A = 1/5.(5/11 - 5/16 + 5/16 - .......5/66)
A = 1/5 . 25/66 = 5/66
25 tháng 3 2015
A=\(\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\)
A=\(\left(\frac{1}{11}-\frac{1}{16}\right)+\left(\frac{1}{16}-\frac{1}{21}\right)+...+\left(\frac{1}{61}-\frac{1}{66}\right)\)
A=\(\frac{1}{11}+\left(\left(\frac{1}{16}-\frac{1}{16}\right)+\left(\frac{1}{21}-\frac{1}{21}\right)+...+\left(\frac{1}{61}-\frac{1}{61}\right)\right)-\frac{1}{66}\)
A=\(\frac{1}{11}+0-\frac{1}{66}\)
A=\(\frac{5}{66}\)
25 tháng 3 2015
A=11-16\11.16+21-16\21.16+...+66-61\61.66
A=1\11-1\16+1\16-...-1\66
A=1\11-1\66
A=5\66
nếu đúng thì like nhé
14 tháng 11 2017
\(B=\frac{5}{11.13}+\frac{5}{16.21}+...+\frac{5}{61.66}\)
\(\Rightarrow B=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\)
\(\Rightarrow B=\frac{1}{11}-\frac{1}{66}\)
\(\Rightarrow B=\frac{5}{66}\)
DH
21 tháng 11 2018
a) \(A=\dfrac{5^2}{11.16}+\dfrac{5^2}{16.21}+\dfrac{5^2}{21.26}+...+\dfrac{5^2}{56.61}\)
\(A=5^2.\left(\dfrac{1}{11.16}+\dfrac{1}{16.21}+\dfrac{1}{21.26}+...+\dfrac{1}{56.61}\right)\)
\(A=\left(5^2:5\right).\left(\dfrac{5}{11.16}+\dfrac{5}{16.21}+\dfrac{5}{21.26}+...+\dfrac{5}{56.61}\right)\)
\(A=5.\left(\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{26}+...+\dfrac{1}{56}-\dfrac{1}{61}\right)\)
\(A=5.\left(\dfrac{1}{11}-\dfrac{1}{61}\right)\)
\(A=5.\dfrac{50}{671}\)
\(Á=\dfrac{250}{671}\)
22 tháng 11 2022
b: \(=-2\left(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{2450}\right)\)
\(=-2\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{49}-\dfrac{1}{50}\right)\)
\(=-2\cdot\dfrac{49}{50}=-\dfrac{49}{25}\)
NT
5
8 tháng 11 2019
\(A=\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\)
\(=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\)
\(=\frac{1}{11}-\frac{1}{66}=\frac{5}{66}\)
8 tháng 11 2019
\(A=\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\)
\(A=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\)
\(A=\frac{1}{11}-\frac{1}{66}\)
\(A=\frac{6}{66}-\frac{1}{66}\)
\(A=\frac{5}{66}\)
DN
4
19 tháng 2 2017
\(A=\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\)
\(=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\)
\(=\frac{1}{11}-\frac{1}{66}\)
\(=\frac{5}{66}\)
Vậy \(A=\frac{5}{66}\)
19 tháng 2 2017
\(A=\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\)
\(=5.\left(\frac{1}{11.16}+\frac{1}{16.21}+...+\frac{1}{61.66}\right)\)
\(=5.\frac{1}{4}.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{24}+...+\frac{1}{61}-\frac{1}{66}\right)\)
\(=\frac{5}{4}.\left(\frac{1}{11}-\frac{1}{66}\right)\)
\(=\frac{5}{4}.\frac{5}{66}\)
\(=\frac{25}{264}\)
C
12 tháng 2 2023
`#lv`
`A=(-1)+(-5)+(-9)+...+(-101)`
`=-(1+5+9+...+101)`
Số số hạng là :
`[101-(-1)]:4+1=26(` số hạng `)`
Tổng là :
`[(-101)+(-1)]xx26:2=-1326`
Vậy `A=-1326`
__
`B=-5/17 . 8/19 + (-12)/17 . 8/19 - 11/19`
`=((-5)/17+(-12)/17).8/19-11/19`
`=-1.8/19-11/19`
`=-8/19-11/19`
`=-8/19+(-11)/19`
`=-19/19`
`=-1`
__
`C=10/1.6 + 10/6.11 + 10/11.16 + ... + 10/2016.2021`
`=2.(1-1/6+1/6-1/11+...+1/2016-1/2021)`
`=2(1-1/2021)`
`=2. (2021/2021-1/2021)`
`=2. 2020/2021`
`=4040/2021`
\(B=\dfrac{5}{11.16}+\dfrac{5}{16.21}+...+\dfrac{5}{61.66}\)
\(B=\dfrac{5}{5}\left(\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+...+\dfrac{1}{61}-\dfrac{1}{66}\right)\)
\(B=\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+...+\dfrac{1}{61}-\dfrac{1}{66}\)
\(B=\dfrac{1}{11}-\dfrac{1}{66}\)
\(B=\dfrac{6}{66}-\dfrac{1}{66}=\dfrac{5}{66}\)