Tính A=1/3+1/6+1/10+1/15+....+1/171+1/190
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12 tháng 4 2019
a (1/6 + 1/10 + 1/15) : (1/6 + 1/10 - 1/15)
= ( 5/30 + 3/30 + 2/30) : (5/30 + 3/30 - 2/30)
= 1/3 : 1/6 = 1/3 x 6/1 = 6/3 = 2
b (1/2 - 1/3 + 1/4 - 1/5) : (1/4 - 1/5)
= (1/2 - 1/3 + 1/4 - 1/5) : (1/4 - 1/5)
= 1/2 - 1/3 = 1/6
T
22 tháng 3 2018
Bạn Kiên giải đúng nhưng chưa rõ nên mình giải lại.
\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{202}{201}\)
\(=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{202}{201}\)
\(=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{x\left(x+1\right)}=\frac{202}{201}\)
\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{\left(x+1\right)}\right)=\frac{202}{201}\)
\(=2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{202}{201}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{\left(x+1\right)}=\frac{202}{201}:2=\frac{202}{402}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{202}{402}=-\frac{1}{402}=\frac{-1}{402}=\frac{1}{-402}\)
\(\Rightarrow\frac{1}{x+1}=\hept{\begin{cases}\frac{-1}{402}\\\frac{1}{-402}\end{cases}}\Rightarrow x+1=\hept{\begin{cases}402\\-402\end{cases}}\Rightarrow\hept{\begin{cases}x=402-1\\x=\left(-402\right)-1\end{cases}}\Rightarrow x=\hept{\begin{cases}401\\-403\end{cases}}\)
22 tháng 3 2018
\(\Rightarrow A=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x.\left(x+1\right)}=\frac{202}{201}\)\(\Rightarrow A=2.\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{202}{201}\)
\(\Rightarrow A=2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{202}{201}\)
\(\Rightarrow A=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{202}{201}\)
\(\Rightarrow A=2.\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{202}{201}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{202}{402}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{202}{402}=\frac{-1}{402}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{-402}\)
\(\Rightarrow x+1=-402\)
\(\Rightarrow x=-403\)
O
19 tháng 6 2021
\(A=\frac{15\times3^{11}+4\times27^4}{9^7}\)
\(A=\frac{15\times177147+4\times531441}{4782969}\)
\(A=\frac{2657205+2125764}{4782969}\)
\(A=\frac{47829969}{47829969}=1\)
14 tháng 4 2016
(1-1/3).(1-1/6).(1-1/10)...(1-1/780) (ko có dấu "...")
Giải: (1-1/3).(1-1/6).(1-1/10)...(1-1/780)
= 2/3 . 5/6....779/780
= 4/6 . 10/12.....1558/1560
= 1.4 . 2.5 .... 38.41/ 2.3 . 3. 4. .....39.40
= ( 1.2.3....38).(4.5....41)/(2.3.4....39)(3...
triệt tiêu xong còn 41/39.3= 41/117
ĐS = 41/117
k cho mh nha bạn
VC
Vũ Cao Minh⁀ᶦᵈᵒᶫ ( ✎﹏IDΣΛ亗 )
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16 tháng 7 2019
\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{9999}{10000}\)
\(A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{99.101}{100.100}\)
\(A=\frac{\left(1.2.3.....99\right).\left(3.4.5.....101\right)}{\left(2.3.4.....100\right).\left(2.3.4.....100\right)}\)
\(A=\frac{1.101}{2.100}=\frac{101}{200}\)
16 tháng 7 2019
\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}......\frac{9999}{10000}\)
\(A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{99.101}{100.100}\)
\(A=\frac{1.2.3.4.....99}{2.3.4.5.....100}.\frac{3.4.5.6.....101}{2.3.4.5.....100}\)
\(A=\frac{1}{100}.\frac{101}{2}\)
\(A=\frac{101}{200}\)
29 tháng 6 2017
\(3^4.5^4-\left(15^2+1\right)\left(15^2-1\right)=\left(3.5\right)^4-\left(15^4-1\right)\)
\(=15^4-15^4+1=1\)
4 tháng 1 2018
a) 25/42 - 20/63 = 5/18
b) ( 9/50 - 13/75 - 1/6 ) : ( -1/2 )2 = -16/25
c) ( 2/15 - 2/65 - 4/39 ) : ( 1/2 - 1/3 )2 = 0
kick và kết bạn với mình nha
=2*(1/6+1/12+1/20+...+1/380)
=2*(1/2*3+1/3*4+1/4*5+...+1/19*20)
=2*(1/2-1/3+1/3-1/4+1/4-1/5+...+1/19-1/20)
=2*(1/2-1/20)
=2*(10/20-1/20)
=2*9/20
=18/20
=9/10
A/2=(1/3+1/6+1/10+1/15+...+1/171+1/190)/2
=1/6+1/12+1/20+1/30+...+1/342+1/380
=1/2.3+1/3.4+1/4.5+1/5.6+....+1/18.19+1/19.20
=1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 +....+ 1/18 - 1/19 + 1/19 - 1/20
=1/2 - 1/20 = 10/20 - 1/20 = 9/20
=> A = 9/20 .2 = 18/20=9/10