1+1/3+1/6+1/10 +...+2/x.(x+1)=1 2019/2021
K
Khách
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NL
2
XO
14 tháng 7 2021
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right)}=\frac{2019}{2021}\)
<=> \(2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2019}{2021}\)
<=> \(2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2019}{2021}\)
<=> \(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2019}{4042}\)
<=> \(\frac{1}{2}-\frac{1}{x+1}=\frac{2019}{2042}\)
<=> \(\frac{1}{x+1}=\frac{1}{2021}\)
<=> x + 1 = 2021
<=> x = 2020
16 tháng 7 2021
Có phải là bình 6a3 học trường THCS Nguyễn Trãi đúng không
NV
Nguyễn Việt Lâm
Giáo viên
25 tháng 3 2021
\(\Leftrightarrow1+\dfrac{2}{2.3}+\dfrac{2}{3.4}+...+\dfrac{2}{x\left(x+1\right)}=1+\dfrac{2019}{2021}\)
\(\Leftrightarrow2\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{x}-\dfrac{1}{x+1}\right)=\dfrac{2019}{2021}\)
\(\Leftrightarrow1-\dfrac{2}{x+1}=\dfrac{2019}{2021}\)
\(\Leftrightarrow\dfrac{2}{x+1}=1-\dfrac{2019}{2021}\)
\(\Leftrightarrow\dfrac{2}{x+1}=\dfrac{2}{2021}\)
\(\Leftrightarrow x+1=2021\)
\(\Leftrightarrow x=2020\)
VQ
5
30 tháng 7 2020
Đề bạn thiếu 1 số \(x\) nữa đúng không?
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2019}{2021}\)
\(\Rightarrow\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}=\frac{2019}{4042}\)
\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}=\frac{2019}{4042}\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2019}{4042}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{2019}{2021}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{2021}\)
\(\Rightarrow x+1=2021\)
\(\Rightarrow x=2020\)
Vậy \(x=2020\).
KN
30 tháng 7 2020
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2019}{2021}\)
\(\Rightarrow2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2019}{2021}\)
\(\Rightarrow\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}=\frac{2019}{4042}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2019}{4042}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2019}{4042}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2019}{4042}=\frac{1}{2021}\)
\(\Leftrightarrow x+1=2021\)
\(\Leftrightarrow x=2020\left(tm:x\in N\right)\)
LD
21 tháng 1 2019
\(1+\dfrac{1}{3}+\dfrac{1}{6}+...+\dfrac{2}{x\left(x+1\right)}=1\dfrac{2019}{2021}\)
\(\Leftrightarrow\dfrac{1}{\dfrac{1\cdot2}{2}}+\dfrac{1}{\dfrac{2\cdot3}{2}}+\dfrac{1}{\dfrac{3\cdot4}{2}}+...+\dfrac{1}{\dfrac{x\left(x+1\right)}{2}}=\dfrac{4040}{2021}\)
\(\Leftrightarrow\dfrac{2}{1\cdot2}+\dfrac{2}{2\cdot3}+\dfrac{2}{3\cdot4}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{4040}{2021}\)
\(\Leftrightarrow2\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{x\left(x+1\right)}\right)=\dfrac{4040}{2021}\)
\(\Leftrightarrow1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{2020}{2021}\)
\(\Leftrightarrow1-\dfrac{1}{x+1}=\dfrac{2020}{2021}\)
\(\Leftrightarrow\dfrac{x}{x+1}=\dfrac{2020}{2021}\)
\(\Leftrightarrow2021x=2020x+2020\Leftrightarrow x=2020\)
Vậy S = {2020}
BL
0
BL
1
B
1
18 tháng 5 2020
( 1/2019 + 2011/2020 + 4012/2021) x (1/2 - 1/3-1/6 )
= ( 1/2019 + 2011/2020 + 4012/2021) x 0
=0
5 tháng 10 2021
Bài 2:
Ta có: \(16x+40=10\cdot3^2+5\left(1+2+3\right)\)
\(\Leftrightarrow16x+40=90+30\)
\(\Leftrightarrow16x=80\)
hay x=5
